Details

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	25%	75%	0%	0%	0%	0
100%	25%	0%	75%	0%	0%	0%	1

Compiler

Compiled 6 to 4 computations (33.3% saved)

sample664.0ms (42.5%)

Results

654.0ms

8256×

body

256

valid

Bogosity

preprocess3.0ms (0.2%)

Algorithm

2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	5
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs
(acosh.f64 x)

Outputs
(acosh.f64 x)

Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify213.0ms (13.7%)

Algorithm

1×	egg-herbie

Rules

1204×	`rational_best_oopsla_all_46_json_45_simplify-10`
1168×	`rational_best_oopsla_all_46_json_45_simplify-89`
1056×	`rational_best_oopsla_all_46_json_45_simplify-74`
834×	`rational_best_oopsla_all_46_json_45_simplify-72`
806×	`rational_best_oopsla_all_46_json_45_simplify-30`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	27
1	18	27
2	34	27
3	89	27
4	345	27
5	1534	27
6	5206	27
7	7193	27

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))

Outputs
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))))

eval1.0ms (0%)

Compiler: Compiled 19 to 12 computations (36.8% saved)

prune1.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

30.5b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	30.5b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))

Compiler

Compiled 10 to 7 computations (30% saved)

localize12.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
✓	0.0b	(-.f64 (*.f64 x x) 1)
✓	0.0b	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
✓	28.4b	(sqrt.f64 (-.f64 (*.f64 x x) 1))

Compiler

Compiled 34 to 17 computations (50% saved)

series4.0ms (0.2%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
1.0ms	x	@	0	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
0.0ms	x	@	0	(sqrt.f64 (-.f64 (*.f64 x x) 1))
0.0ms	x	@	-inf	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
0.0ms	x	@	inf	(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite90.0ms (5.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1158×	`rational_best_oopsla_all_46_json-2`
1158×	`rational_best_oopsla_all_46_json-1`
1158×	`rational_best_oopsla_all_46_json-4`
1158×	`rational_best_oopsla_all_46_json-3`
1138×	`rational_best_oopsla_all_46_json_45_simplify-89`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	80
1	59	80
2	153	80
3	522	80
4	2356	80

Stop Event

1×	node limit

Counts

4 → 170

Calls

Call 1

Inputs
(sqrt.f64 (-.f64 (*.f64 x x) 1))
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
(-.f64 (*.f64 x x) 1)
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))

Outputs
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(+.f64 (.f64 x x) -1))))) (/.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (/.f64 (/.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (/.f64 1 (/.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))))) (/.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (/.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))))) (neg.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (/.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))))) (.f64 (neg.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))) (/.f64 (/.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))) (/.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (/.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (/.f64 (/.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))) (/.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (/.f64 (.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (/.f64 1 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))))) (.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (/.f64 1 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))))))))

simplify83.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

1420×	`rational_best_oopsla_all_46_json_45_simplify-89`
1330×	`rational_best_oopsla_all_46_json_45_simplify-37`
1140×	`rational_best_oopsla_all_46_json_45_simplify-24`
1124×	`rational_best_oopsla_all_46_json_45_simplify-74`
718×	`rational_best_oopsla_all_46_json_45_simplify-49`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	404	5126
1	1567	5110

Stop Event

1×	node limit

Counts

218 → 252

Calls

Call 1

Inputs
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (*.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5))))))
x
(-.f64 x (*.f64 1/2 (/.f64 1 x)))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))))
(*.f64 -1 x)
(+.f64 (.f64 -1 x) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 -1 x)))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (.f64 -1 x))))
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) x)
(+.f64 (sqrt.f64 -1) (+.f64 (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) x))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) x)))
(*.f64 2 x)
(-.f64 (.f64 2 x) (.f64 1/2 (/.f64 1 x)))
(-.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 1 x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
(-.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (.f64 1/8 (/.f64 1 (pow.f64 x 3))))))
(/.f64 1/2 x)
(+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 1/2 (/.f64 1 x))))
(+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 5/128 (/.f64 1 (pow.f64 x 7))))))
-1
(-.f64 (pow.f64 x 2) 1)
(-.f64 (pow.f64 x 2) 1)
(-.f64 (pow.f64 x 2) 1)
(pow.f64 x 2)
(-.f64 (pow.f64 x 2) 1)
(-.f64 (pow.f64 x 2) 1)
(-.f64 (pow.f64 x 2) 1)
(pow.f64 x 2)
(-.f64 (pow.f64 x 2) 1)
(-.f64 (pow.f64 x 2) 1)
(-.f64 (pow.f64 x 2) 1)
(log.f64 (sqrt.f64 -1))
(+.f64 (/.f64 x (sqrt.f64 -1)) (log.f64 (sqrt.f64 -1)))
(+.f64 (*.f64 -1/6 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (/.f64 x (sqrt.f64 -1)) (log.f64 (sqrt.f64 -1))))
(+.f64 (.f64 3/40 (/.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 5))) (+.f64 (.f64 -1/6 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (/.f64 x (sqrt.f64 -1)) (log.f64 (sqrt.f64 -1)))))
(+.f64 (log.f64 2) (*.f64 -1 (log.f64 (/.f64 1 x))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 2)) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 2)) (+.f64 (.f64 3/32 (/.f64 1 (pow.f64 x 4))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 2)) (+.f64 (.f64 3/32 (/.f64 1 (pow.f64 x 4))) (+.f64 (.f64 5/96 (/.f64 1 (pow.f64 x 6))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))))
(+.f64 (log.f64 -1/2) (log.f64 (/.f64 -1 x)))
(+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 -1/2) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))
(+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 -1/2) (+.f64 (.f64 3/32 (/.f64 1 (pow.f64 x 4))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))))
(+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (log.f64 -1/2) (+.f64 (.f64 3/32 (/.f64 1 (pow.f64 x 4))) (+.f64 (.f64 5/96 (/.f64 1 (pow.f64 x 6))) (*.f64 1/4 (/.f64 1 (pow.f64 x 2)))))))
(+.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 0)
(+.f64 0 (sqrt.f64 (+.f64 (*.f64 x x) -1)))
(-.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 0)
(-.f64 0 (neg.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1))))
(.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))
(.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) 1)
(.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1))))
(.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))
(.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (*.f64 x x) -1)))))
(.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (/.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1)))))
(.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (/.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1))) (sqrt.f64 (+.f64 (*.f64 x x) -1)))))
(.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1))) (.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))))))
(.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1))) (.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1))))))
(.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (/.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (sqrt.f64 (+.f64 (.f64 x x) -1)))))
(.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (/.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1)))) (sqrt.f64 (+.f64 (.f64 x x) -1)))))
(.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1))) (.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))))) (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (*.f64 x x) -1)))))
(.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1))) (.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1))))) (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (*.f64 x x) -1)))))
(.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (/.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1))) (sqrt.f64 (+.f64 (.f64 x x) -1)))) (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1)))))
(.f64 -1 (neg.f64 (sqrt.f64 (+.f64 (.f64 x x) -1))))
(.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1))) (sqrt.f64 (+.f64 (.f64 x x) -1)))
(.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1))) (.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (/.f64 1 (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (*.f64 x x) -1))))))
(.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1))) (.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (/.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1)))) (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1))))))
(.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1))) (.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (/.f64 1 (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1))))) (/.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1))))))
(.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (sqrt.f64 (+.f64 (*.f64 x x) -1)))
(.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (/.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))))))
(.f64 (neg.f64 (sqrt.f64 (+.f64 (.f64 x x) -1))) -1)
(.f64 (neg.f64 (sqrt.f64 (+.f64 (.f64 x x) -1))) (neg.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1)))))
(.f64 (neg.f64 (sqrt.f64 (+.f64 (.f64 x x) -1))) (.f64 -1 (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (*.f64 x x) -1)))))
(.f64 (neg.f64 (sqrt.f64 (+.f64 (.f64 x x) -1))) (.f64 (neg.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1)))) (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (*.f64 x x) -1)))))
(.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1)))) (sqrt.f64 (+.f64 (*.f64 x x) -1)))
(.f64 (/.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1)))) (sqrt.f64 (+.f64 (.f64 x x) -1)))
(.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (/.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1))) (sqrt.f64 (+.f64 (.f64 x x) -1)))) (sqrt.f64 (+.f64 (*.f64 x x) -1)))
(.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (/.f64 1 (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1))))) (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (*.f64 x x) -1))))
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(.f64 -1 (neg.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))))
(.f64 (/.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))))
(.f64 (/.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))) (.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (/.f64 1 (/.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))))))))
(.f64 (/.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))) (.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (/.f64 (.f64 (/.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))) (/.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))))) (/.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))))))
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(.f64 (neg.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))) (.f64 (neg.f64 (/.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))))) (/.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1)))))))
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(.f64 (.f64 (/.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))) (.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (/.f64 1 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))))
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(/.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1)))) 1)
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(neg.f64 (neg.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))))))

Outputs
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))))
(+.f64 (sqrt.f64 -1) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))))
(+.f64 (sqrt.f64 -1) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3)))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (*.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5))))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (+.f64 (sqrt.f64 -1) (*.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5))))))
(+.f64 (sqrt.f64 -1) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (*.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))))))
x
(-.f64 x (*.f64 1/2 (/.f64 1 x)))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 1/16 (/.f64 1 (pow.f64 x 5))))))
(*.f64 -1 x)
(neg.f64 x)
(+.f64 (.f64 -1 x) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 -1 x))
(+.f64 (*.f64 1/2 (/.f64 1 x)) (neg.f64 x))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 -1 x)))
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(.f64 (.f64 (/.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))) (.f64 (/.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))) (/.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))))
(log.f64 (+.f64 x (sqrt.f64 (+.f64 -1 (*.f64 x x)))))
(.f64 (/.f64 (/.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))) (/.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))))
(log.f64 (+.f64 x (sqrt.f64 (+.f64 -1 (*.f64 x x)))))
(.f64 (.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (/.f64 (/.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1)))))
(log.f64 (+.f64 x (sqrt.f64 (+.f64 -1 (*.f64 x x)))))
(.f64 (.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (/.f64 1 (/.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))))) (/.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))))))
(log.f64 (+.f64 x (sqrt.f64 (+.f64 -1 (*.f64 x x)))))
(.f64 (neg.f64 (/.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))))) (neg.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))))
(log.f64 (+.f64 x (sqrt.f64 (+.f64 -1 (*.f64 x x)))))
(.f64 (neg.f64 (/.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))))) (.f64 (neg.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))) (/.f64 (/.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))) (/.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))))))))
(log.f64 (+.f64 x (sqrt.f64 (+.f64 -1 (*.f64 x x)))))
(/.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1)))) 1)
(log.f64 (+.f64 x (sqrt.f64 (+.f64 -1 (*.f64 x x)))))
(/.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (/.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))))))
(log.f64 (+.f64 x (sqrt.f64 (+.f64 -1 (*.f64 x x)))))
(/.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (/.f64 (/.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))) (/.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1)))))))
(log.f64 (+.f64 x (sqrt.f64 (+.f64 -1 (*.f64 x x)))))
(/.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (/.f64 (.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (/.f64 1 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))))) (.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (/.f64 1 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))))))))
(log.f64 (+.f64 x (sqrt.f64 (+.f64 -1 (*.f64 x x)))))
(neg.f64 (neg.f64 (log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))))))
(log.f64 (+.f64 x (sqrt.f64 (+.f64 -1 (*.f64 x x)))))

eval231.0ms (14.8%)

Compiler: Compiled 7777 to 4888 computations (37.1% saved)

prune81.0ms (5.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	250	2	252
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	250	3	253

Error

0.0b

Counts

253 → 3

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.4b	(log.f64 (-.f64 (.f64 x 2) (.f64 1/2 (/.f64 1 x))))
✓	30.5b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
▶	0.5b	(log.f64 (+.f64 x x))

Compiler

Compiled 26 to 19 computations (26.9% saved)

localize4.0ms (0.3%)

Compiler: Compiled 9 to 3 computations (66.7% saved)

localize14.0ms (0.9%)

Compiler: Compiled 35 to 27 computations (22.9% saved)

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	2	2
Total	3	3

Error

0.0b

Counts

3 → 3

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.4b	(log.f64 (-.f64 (.f64 x 2) (.f64 1/2 (/.f64 1 x))))
✓	30.5b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
✓	0.5b	(log.f64 (+.f64 x x))

Compiler

Compiled 26 to 19 computations (26.9% saved)

regimes65.0ms (4.2%)

Accuracy

Total -30.6b remaining (-8003.5%)

Threshold costs -30.6b (-8003.5%)

Counts

3 → 1

Calls

Call 1

Inputs
(log.f64 (+.f64 x x))
(log.f64 (-.f64 (.f64 x 2) (.f64 1/2 (/.f64 1 x))))
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))

Outputs
(log.f64 (-.f64 (.f64 x 2) (.f64 1/2 (/.f64 1 x))))

Calls

3 calls:

58.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
3.0ms	x
3.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))

Results

Error	Segments	Branch
0.4b	1	`x`
0.4b	1	`(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))`
0.4b	1	`(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))`

Compiler

Compiled 45 to 31 computations (31.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	40

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(log.f64 (-.f64 (.f64 x 2) (.f64 1/2 (/.f64 1 x))))
(log.f64 (+.f64 x x))

Outputs
(log.f64 (-.f64 (.f64 x 2) (.f64 1/2 (/.f64 1 x))))
(log.f64 (+.f64 x x))

Compiler

Compiled 16 to 12 computations (25% saved)

soundness74.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

1420×	`rational_best_oopsla_all_46_json_45_simplify-89`
1330×	`rational_best_oopsla_all_46_json_45_simplify-37`
1140×	`rational_best_oopsla_all_46_json_45_simplify-24`
1124×	`rational_best_oopsla_all_46_json_45_simplify-74`
718×	`rational_best_oopsla_all_46_json_45_simplify-49`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	404	5126
1	1567	5110

Stop Event

1×	node limit

Compiler

Compiled 21 to 17 computations (19% saved)

end17.0ms (1.1%)

Compiler: Compiled 15 to 11 computations (26.7% saved)

Details

analyze0.0ms (0%)

sample664.0ms (42.5%)

preprocess3.0ms (0.2%)

simplify213.0ms (13.7%)

eval1.0ms (0%)

prune1.0ms (0.1%)

localize12.0ms (0.8%)

series4.0ms (0.2%)

rewrite90.0ms (5.8%)

simplify83.0ms (5.3%)

eval231.0ms (14.8%)

prune81.0ms (5.2%)

localize4.0ms (0.3%)

localize14.0ms (0.9%)

eval0.0ms (0%)

prune1.0ms (0.1%)

regimes65.0ms (4.2%)

simplify2.0ms (0.1%)

soundness74.0ms (4.7%)

end17.0ms (1.1%)

Profiling