Details

analyze249.0ms (5.3%)

Algorithm

1×

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
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	68.7%	6.3%	6
25%	56.2%	18.8%	7
25%	48.4%	26.6%	8
25%	35.1%	39.9%	9
28.1%	18.3%	53.6%	10
31.6%	12.3%	56.1%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 34 to 22 computations (35.3% saved)

sample29.0ms (0.6%)

Algorithm

1×

intervals

Results

20.0ms

256×

body

128

valid

Compiler

Compiled 69 to 45 computations (34.8% saved)

simplify66.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

669×	`unsub-neg_binary64`
596×	`cancel-sign-sub-inv_binary64`
373×	`neg-sub0_binary64`
373×	`neg-mul-1_binary64`
340×	`+-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	46
1	61	46
2	152	46
3	438	46
4	1297	46
5	2510	46
6	4609	46
7	5033	46

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)

Compiler

Compiled 99 to 63 computations (36.4% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
0.1b	(.f64 (.f64 a a) (+.f64 1 a))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
0.6b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

rewrite130.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

15×	`add-exp-log_binary64`
15×	`pow1_binary64`
14×	`add-cbrt-cube_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`

Counts

4 → 80

Calls

4 calls:

9.0ms	(.f64 (.f64 a a) (+.f64 1 a))
6.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
6.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
4.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

Compiler

Compiled 3111 to 1674 computations (46.2% saved)

series186.0ms (3.9%)

Error

0.0b

Counts

4 → 53

Calls

4 calls:

70.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
46.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
24.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
13.0ms	(.f64 (.f64 a a) (+.f64 1 a))

Compiler

Compiled 3014 to 2236 computations (25.8% saved)

simplify82.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

853×	`distribute-rgt-in_binary64`
794×	`distribute-lft-in_binary64`
271×	`cancel-sign-sub-inv_binary64`
246×	`associate-l_binary64`
204×	`associate-r_binary64`

Counts

133 → 105

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	190	3004
1	532	2684
2	1769	2599
3	5465	2599

prune93.0ms (2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	101	4	105
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	101	5	106

Error

0.0b

Counts

106 → 5

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 (+.f64 (+.f64 (+.f64 (pow.f64 b 4) (.f64 2 (.f64 a (.f64 a (.f64 b b))))) (pow.f64 a 4)) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
✓	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
	11.7b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (log.f64 (exp.f64 (+.f64 (.f64 a a) (pow.f64 a 3)))) (.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))))) 1)
	0.5b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2)) (cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))) (cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
	0.2b	(-.f64 (+.f64 (.f64 4 (.f64 a a)) (+.f64 (.f64 (pow.f64 a 3) (+.f64 a 4)) (.f64 (.f64 b b) (+.f64 (+.f64 (.f64 2 (.f64 a a)) 4) (+.f64 (.f64 b b) (*.f64 a -12)))))) 1)

Compiler

Compiled 2559 to 1421 computations (44.5% saved)

localize24.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 a a) (+.f64 1 a))
0.6b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
0.7b	(.f64 a (.f64 b b))
1.3b	(.f64 a (.f64 a (*.f64 b b)))

rewrite176.0ms (3.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

28×	`add-cbrt-cube_binary64`
28×	`add-exp-log_binary64`
28×	`pow1_binary64`
15×	`cbrt-unprod_binary64`
15×	`prod-exp_binary64`

Counts

4 → 89

Calls

4 calls:

8.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
7.0ms	(.f64 (.f64 a a) (+.f64 1 a))
6.0ms	(.f64 a (.f64 a (*.f64 b b)))
4.0ms	(.f64 a (.f64 b b))

Compiler

Compiled 3577 to 2031 computations (43.2% saved)

series90.0ms (1.9%)

Error

0.0b

Counts

4 → 26

Calls

4 calls:

24.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
20.0ms	(.f64 a (.f64 a (*.f64 b b)))
18.0ms	(.f64 a (.f64 b b))
12.0ms	(.f64 (.f64 a a) (+.f64 1 a))

Compiler

Compiled 2254 to 1615 computations (28.3% saved)

simplify91.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

471×	`*-commutative_binary64`
355×	`distribute-rgt-in_binary64`
316×	`distribute-lft-in_binary64`
300×	`associate-l_binary64`
299×	`sqr-pow_binary64`

Counts

115 → 94

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	138	1575
1	360	1304
2	1266	1265
3	2699	1239
4	3867	1228
5	5117	1228

prune99.0ms (2.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	94	5	99

Error

0.0b

Counts

99 → 5

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (+.f64 (+.f64 (+.f64 (pow.f64 b 4) (.f64 2 (.f64 a (.f64 a (.f64 b b))))) (pow.f64 a 4)) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
✓	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
	11.7b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (log.f64 (exp.f64 (+.f64 (.f64 a a) (pow.f64 a 3)))) (.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))))) 1)
	0.5b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2)) (cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))) (cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
▶	0.2b	(-.f64 (+.f64 (.f64 4 (.f64 a a)) (+.f64 (.f64 (pow.f64 a 3) (+.f64 a 4)) (.f64 (.f64 b b) (+.f64 (+.f64 (.f64 2 (.f64 a a)) 4) (+.f64 (.f64 b b) (*.f64 a -12)))))) 1)

Compiler

Compiled 2389 to 1420 computations (40.6% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (+.f64 (.f64 2 (.f64 a a)) 4) (+.f64 (.f64 b b) (.f64 a -12)))
0.0b	(+.f64 (.f64 b b) (.f64 a -12))
0.1b	(*.f64 (pow.f64 a 3) (+.f64 a 4))
2.0b	(.f64 (.f64 b b) (+.f64 (+.f64 (.f64 2 (.f64 a a)) 4) (+.f64 (.f64 b b) (.f64 a -12))))

rewrite205.0ms (4.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

18×	`add-log-exp_binary64`
17×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64`
14×	`add-exp-log_binary64`
13×	`associate-l_binary64`

Counts

4 → 96

Calls

4 calls:

17.0ms	(.f64 (.f64 b b) (+.f64 (+.f64 (.f64 2 (.f64 a a)) 4) (+.f64 (.f64 b b) (.f64 a -12))))
15.0ms	(+.f64 (+.f64 (.f64 2 (.f64 a a)) 4) (+.f64 (.f64 b b) (.f64 a -12)))
7.0ms	(*.f64 (pow.f64 a 3) (+.f64 a 4))
3.0ms	(+.f64 (.f64 b b) (.f64 a -12))

Compiler

Compiled 4462 to 2604 computations (41.6% saved)

series149.0ms (3.2%)

Error

0.0b

Counts

4 → 43

Calls

4 calls:

51.0ms	(.f64 (.f64 b b) (+.f64 (+.f64 (.f64 2 (.f64 a a)) 4) (+.f64 (.f64 b b) (.f64 a -12))))
31.0ms	(+.f64 (+.f64 (.f64 2 (.f64 a a)) 4) (+.f64 (.f64 b b) (.f64 a -12)))
17.0ms	(+.f64 (.f64 b b) (.f64 a -12))
13.0ms	(*.f64 (pow.f64 a 3) (+.f64 a 4))

Compiler

Compiled 2871 to 2069 computations (27.9% saved)

simplify158.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

484×	`exp-prod_binary64`
424×	`associate-l_binary64`
388×	`associate-r_binary64`
347×	`cancel-sign-sub-inv_binary64`
250×	`distribute-rgt-in_binary64`

Counts

139 → 107

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	204	3416
1	666	2921
2	2934	2909
3	4487	2885
4	4961	2885
5	4964	2885

prune112.0ms (2.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	107	5	112

Error

0.0b

Counts

112 → 5

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (+.f64 (+.f64 (+.f64 (pow.f64 b 4) (.f64 2 (.f64 a (.f64 a (.f64 b b))))) (pow.f64 a 4)) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
✓	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
	11.7b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (log.f64 (exp.f64 (+.f64 (.f64 a a) (pow.f64 a 3)))) (.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))))) 1)
▶	0.5b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2)) (cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))) (cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
✓	0.2b	(-.f64 (+.f64 (.f64 4 (.f64 a a)) (+.f64 (.f64 (pow.f64 a 3) (+.f64 a 4)) (.f64 (.f64 b b) (+.f64 (+.f64 (.f64 2 (.f64 a a)) 4) (+.f64 (.f64 b b) (*.f64 a -12)))))) 1)

Compiler

Compiled 3082 to 1899 computations (38.4% saved)

localize23.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.6b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
19.7b	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))
19.7b	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))
19.7b	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))

rewrite152.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

24×	`cbrt-prod_binary64`
12×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
9×	`unpow-prod-down_binary64`

Counts

4 → 73

Calls

4 calls:

6.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
6.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))
4.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))
4.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))

Compiler

Compiled 4552 to 2144 computations (52.9% saved)

series311.0ms (6.6%)

Error

0.0b

Counts

4 → 53

Calls

4 calls:

123.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))
68.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))
62.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))
25.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

Compiler

Compiled 6246 to 4010 computations (35.8% saved)

simplify152.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

452×	`associate-+l+_binary64`
336×	`unswap-sqr_binary64`
253×	`neg-mul-1_binary64`
249×	`neg-sub0_binary64`
242×	`*-commutative_binary64`

Counts

126 → 114

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	116	2648
1	272	2417
2	799	2417
3	1645	2417
4	4213	2417
5	4817	2417
6	4915	2417

prune101.0ms (2.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	114	5	119

Error

0.0b

Counts

119 → 5

Alt Table

Status	Error	Program
	0.0b	(-.f64 (+.f64 (+.f64 (+.f64 (pow.f64 b 4) (.f64 2 (.f64 a (.f64 a (.f64 b b))))) (pow.f64 a 4)) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
	11.7b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (log.f64 (exp.f64 (+.f64 (.f64 a a) (pow.f64 a 3)))) (.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))))) 1)
	0.5b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2)) (cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))) (cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
	0.2b	(-.f64 (+.f64 (.f64 4 (.f64 a a)) (+.f64 (.f64 (pow.f64 a 3) (+.f64 a 4)) (.f64 (.f64 b b) (+.f64 (+.f64 (.f64 2 (.f64 a a)) 4) (+.f64 (.f64 b b) (*.f64 a -12)))))) 1)

Compiler

Compiled 3382 to 1688 computations (50.1% saved)

regimes885.0ms (18.7%)

Accuracy

Total 0.0b remaining (83.3%)

Threshold costs 0.0b (83.3%)

Compiler

Compiled 25606 to 16887 computations (34.1% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
5×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	49
1	36	49
2	37	49
3	35	49

end1.0ms (0%)

Compiler: Compiled 35 to 23 computations (34.3% saved)

sample1.1s (23.7%)

Algorithm

1×

intervals

Results

709.0ms	8000×	body	128	valid
1.0ms	10×	body	128	invalid

Compiler

Compiled 273 to 173 computations (36.6% saved)

Details

analyze249.0ms (5.3%)

sample29.0ms (0.6%)

simplify66.0ms (1.4%)

prune3.0ms (0.1%)

localize18.0ms (0.4%)

rewrite130.0ms (2.8%)

series186.0ms (3.9%)

simplify82.0ms (1.7%)

prune93.0ms (2%)

localize24.0ms (0.5%)

rewrite176.0ms (3.7%)

series90.0ms (1.9%)

simplify91.0ms (1.9%)

prune99.0ms (2.1%)

localize18.0ms (0.4%)

rewrite205.0ms (4.3%)

series149.0ms (3.2%)

simplify158.0ms (3.3%)

prune112.0ms (2.4%)

localize23.0ms (0.5%)

rewrite152.0ms (3.2%)

series311.0ms (6.6%)

simplify152.0ms (3.2%)

prune101.0ms (2.1%)

regimes885.0ms (18.7%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.1s (23.7%)

Profiling