Details

analyze460.0ms (4.9%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	8	20
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
25%	74.9%	0.1%	4
50%	50%	0.1%	5
50%	37.5%	12.6%	6
50%	25%	25.1%	7
50%	18.7%	31.3%	8
50%	12.5%	37.6%	9
50%	9.4%	40.7%	10
50%	6.2%	43.8%	11
50%	4.7%	45.4%	12
50%	3.1%	46.9%	13
50%	2.3%	47.7%	14

Symmetry

(sort a b)

Compiler

Compiled 7 to 7 computations (0% saved)

sample83.0ms (0.9%)

Algorithm

1×

intervals

Results

29.0ms	51×	body	1024	valid
9.0ms	32×	body	512	valid
9.0ms	162×	body	128	valid
2.0ms	3×	body	2048	valid
1.0ms	8×	body	256	valid
0.0ms	6×	body	128	overflowed

Compiler

Compiled 13 to 15 computations (-15.4% saved)

simplify14.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	8	10
1	8	10

prune7.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

25.6b

Counts

2 → 1

Compiler

Compiled 12 to 12 computations (0% saved)

localize14.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
3.7b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

rewrite36.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

25.6b

Rules

7×	`*-un-lft-identity_binary64`
4×	`log-prod_binary64` `add-log-exp_binary64`
3×	`pow1_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `add-exp-log_binary64`
2×	`flip3-+_binary64` `log-div_binary64` `flip-+_binary64` `distribute-lft-out_binary64` `add-cbrt-cube_binary64`
1×	`log-pow_binary64` `rem-log-exp_binary64` `sum-log_binary64` `+-commutative_binary64`

Counts

2 → 27

Calls

2 calls:

7.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
4.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

Compiler

Compiled 363 to 92 computations (74.7% saved)

series270.0ms (2.8%)

Error

0.6b

Counts

2 → 21

Calls

2 calls:

207.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
37.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

Compiler

Compiled 700 to 529 computations (24.4% saved)

simplify90.0ms (1%)

Algorithm

1×	egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	5221	784

prune51.0ms (0.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	44	4	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	4	49

Error

0.6b

Counts

49 → 4

Compiler

Compiled 647 to 282 computations (56.4% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (.f64 (/.f64 b (+.f64 1 (exp.f64 a))) b) (+.f64 1/2 (/.f64 -1/2 (+.f64 1 (exp.f64 a)))))
0.0b	(+.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (+.f64 (.f64 (.f64 (/.f64 b (+.f64 1 (exp.f64 a))) b) (+.f64 1/2 (/.f64 -1/2 (+.f64 1 (exp.f64 a))))) (log.f64 (+.f64 1 (exp.f64 a)))))
0.0b	(+.f64 (.f64 (.f64 (/.f64 b (+.f64 1 (exp.f64 a))) b) (+.f64 1/2 (/.f64 -1/2 (+.f64 1 (exp.f64 a))))) (log.f64 (+.f64 1 (exp.f64 a))))
0.0b	(+.f64 1/2 (/.f64 -1/2 (+.f64 1 (exp.f64 a))))

rewrite299.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

14×	`*-un-lft-identity_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`add-log-exp_binary64`
9×	`pow1_binary64`
8×	`flip3-+_binary64` `flip-+_binary64`
6×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `associate-+r-_binary64`
5×	`sum-log_binary64` `associate-+r+_binary64` `prod-exp_binary64` `cbrt-unprod_binary64`
4×	`distribute-lft-out_binary64` `log-div_binary64` `log-prod_binary64` `associate-l/_binary64` `associate-r*_binary64`
3×	`+-commutative_binary64` `pow-prod-down_binary64`
2×	`distribute-rgt-in_binary64` `associate-+l+_binary64` `distribute-lft-in_binary64` `frac-add_binary64` `frac-times_binary64` `associate-*r/_binary64`
1×	`div-exp_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `*-commutative_binary64`

Counts

4 → 77

Calls

4 calls:

40.0ms	(+.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (+.f64 (.f64 (.f64 (/.f64 b (+.f64 1 (exp.f64 a))) b) (+.f64 1/2 (/.f64 -1/2 (+.f64 1 (exp.f64 a))))) (log.f64 (+.f64 1 (exp.f64 a)))))
32.0ms	(+.f64 (.f64 (.f64 (/.f64 b (+.f64 1 (exp.f64 a))) b) (+.f64 1/2 (/.f64 -1/2 (+.f64 1 (exp.f64 a))))) (log.f64 (+.f64 1 (exp.f64 a))))
20.0ms	(.f64 (.f64 (/.f64 b (+.f64 1 (exp.f64 a))) b) (+.f64 1/2 (/.f64 -1/2 (+.f64 1 (exp.f64 a)))))
13.0ms	(+.f64 1/2 (/.f64 -1/2 (+.f64 1 (exp.f64 a))))

Compiler

Compiled 3738 to 2462 computations (34.1% saved)

series1.7s (17.9%)

Error

0.6b

Counts

4 → 37

Calls

4 calls:

708.0ms	(+.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (+.f64 (.f64 (.f64 (/.f64 b (+.f64 1 (exp.f64 a))) b) (+.f64 1/2 (/.f64 -1/2 (+.f64 1 (exp.f64 a))))) (log.f64 (+.f64 1 (exp.f64 a)))))
594.0ms	(+.f64 (.f64 (.f64 (/.f64 b (+.f64 1 (exp.f64 a))) b) (+.f64 1/2 (/.f64 -1/2 (+.f64 1 (exp.f64 a))))) (log.f64 (+.f64 1 (exp.f64 a))))
260.0ms	(.f64 (.f64 (/.f64 b (+.f64 1 (exp.f64 a))) b) (+.f64 1/2 (/.f64 -1/2 (+.f64 1 (exp.f64 a)))))
72.0ms	(+.f64 1/2 (/.f64 -1/2 (+.f64 1 (exp.f64 a))))

Compiler

Compiled 2835 to 2163 computations (23.7% saved)

simplify137.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	4946	4028
1	4946	4028

prune250.0ms (2.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	113	5	118

Error

0.6b

Counts

118 → 5

Compiler

Compiled 4184 to 2703 computations (35.4% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(log.f64 (+.f64 1 (exp.f64 a)))
0.0b	(+.f64 1 (exp.f64 a))
0.0b	(+.f64 1 (exp.f64 a))
0.0b	(+.f64 (log.f64 (+.f64 1 (exp.f64 a))) (/.f64 b (+.f64 1 (exp.f64 a))))

rewrite112.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

17×	`*-un-lft-identity_binary64`
9×	`add-log-exp_binary64`
8×	`log-prod_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `distribute-lft-out_binary64`
5×	`add-exp-log_binary64` `flip3-+_binary64` `flip-+_binary64`
4×	`add-cbrt-cube_binary64` `log-div_binary64` `associate-+l+_binary64`
3×	`sum-log_binary64` `+-commutative_binary64`
2×	`log-pow_binary64` `associate-+l-_binary64`
1×	`rem-log-exp_binary64`

Counts

4 → 58

Calls

4 calls:

14.0ms	(+.f64 (log.f64 (+.f64 1 (exp.f64 a))) (/.f64 b (+.f64 1 (exp.f64 a))))
4.0ms	(+.f64 1 (exp.f64 a))
4.0ms	(log.f64 (+.f64 1 (exp.f64 a)))
4.0ms	(+.f64 1 (exp.f64 a))

Compiler

Compiled 1159 to 732 computations (36.8% saved)

series382.0ms (4%)

Error

0.6b

Counts

4 → 24

Calls

4 calls:

258.0ms	(+.f64 (log.f64 (+.f64 1 (exp.f64 a))) (/.f64 b (+.f64 1 (exp.f64 a))))
77.0ms	(log.f64 (+.f64 1 (exp.f64 a)))
12.0ms	(+.f64 1 (exp.f64 a))
10.0ms	(+.f64 1 (exp.f64 a))

Compiler

Compiled 766 to 605 computations (21% saved)

simplify117.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	4971	1188
1	4971	1188

prune93.0ms (1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	79	3	82
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	80	7	87

Error

0.6b

Counts

87 → 7

Compiler

Compiled 1465 to 959 computations (34.5% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (*.f64 b b) (+.f64 1 (exp.f64 a)))
0.0b	(-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 a))))
0.6b	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 a))))
0.6b	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 a))))

rewrite315.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

34×	`*-un-lft-identity_binary64`
23×	`add-sqr-sqrt_binary64`
18×	`add-cube-cbrt_binary64` `cancel-sign-sub-inv_binary64`
17×	`times-frac_binary64`
14×	`log-prod_binary64`
11×	`add-exp-log_binary64`
9×	`add-cbrt-cube_binary64`
8×	`pow1_binary64` `sqrt-prod_binary64`
7×	`distribute-lft-out_binary64`
6×	`log-pow_binary64` `add-log-exp_binary64`
4×	`flip3-+_binary64` `sqrt-div_binary64` `log-div_binary64` `flip-+_binary64` `associate-/r/_binary64` `associate-/r*_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-log-exp_binary64` `difference-of-squares_binary64` `div-inv_binary64` `div-exp_binary64` `cbrt-undiv_binary64`
1×	`diff-log_binary64` `flip3--_binary64` `sub-neg_binary64` `flip--_binary64` `distribute-lft-out--_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `frac-2neg_binary64` `clear-num_binary64` `associate-/l*_binary64`

Counts

4 → 97

Calls

4 calls:

12.0ms	(/.f64 (*.f64 b b) (+.f64 1 (exp.f64 a)))
12.0ms	(-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 a))))
5.0ms	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 a))))
5.0ms	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 a))))

Compiler

Compiled 4512 to 2967 computations (34.2% saved)

series475.0ms (5%)

Error

0.6b

Counts

4 → 22

Calls

4 calls:

130.0ms	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 a))))
119.0ms	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 a))))
118.0ms	(/.f64 (*.f64 b b) (+.f64 1 (exp.f64 a)))
60.0ms	(-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 a))))

Compiler

Compiled 2528 to 1900 computations (24.8% saved)

simplify119.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	4818	1797
1	4818	1797

prune298.0ms (3.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	119	7	126

Error

0.6b

Counts

126 → 7

Compiler

Compiled 5053 to 3302 computations (34.7% saved)

regimes556.0ms (5.9%)

Accuracy

Total 0.4b remaining (37.2%)

Threshold costs 0.4b (37.2%)

Compiler

Compiled 5612 to 4279 computations (23.8% saved)

bsearch0.0ms (0%)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	47
1	23	47

Compiler

Compiled 60 to 44 computations (26.7% saved)

end0.0ms (0%)

sample3.6s (37.4%)

Algorithm

1×

intervals

Results

1.1s	1962×	body	1024	valid
279.0ms	963×	body	512	valid
239.0ms	4462×	body	128	valid
123.0ms	165×	body	2048	valid
70.0ms	448×	body	256	valid
7.0ms	144×	body	128	overflowed

Compiler

Compiled 909 to 698 computations (23.2% saved)

Details

analyze460.0ms (4.9%)

sample83.0ms (0.9%)

simplify14.0ms (0.2%)

prune7.0ms (0.1%)

localize14.0ms (0.1%)

rewrite36.0ms (0.4%)

series270.0ms (2.8%)

simplify90.0ms (1%)

prune51.0ms (0.5%)

localize15.0ms (0.2%)

rewrite299.0ms (3.1%)

series1.7s (17.9%)

simplify137.0ms (1.4%)

prune250.0ms (2.6%)

localize14.0ms (0.1%)

rewrite112.0ms (1.2%)

series382.0ms (4%)

simplify117.0ms (1.2%)

prune93.0ms (1%)

localize19.0ms (0.2%)

rewrite315.0ms (3.3%)

series475.0ms (5%)

simplify119.0ms (1.3%)

prune298.0ms (3.1%)

regimes556.0ms (5.9%)

bsearch0.0ms (0%)

simplify11.0ms (0.1%)

end0.0ms (0%)

sample3.6s (37.4%)

Profiling