Details

analyze1.6s (16%)

Algorithm

1×

Search

True	Other	False	Iter
0%	49.9%	50.1%	0
0%	49.9%	50.1%	1
0%	49.9%	50.1%	2
0%	49.9%	50.1%	3
0%	49.9%	50.1%	4
0%	49.9%	50.1%	5
0%	49.9%	50.1%	6
0%	49.9%	50.1%	7
0%	49.9%	50.1%	8
0.4%	49.5%	50.1%	9
0.4%	49.3%	50.3%	10
0.6%	48.9%	50.5%	11
1.1%	48.1%	50.9%	12
1.5%	47.3%	51.2%	13
1.7%	46.9%	51.5%	14

Compiler

Compiled 31 to 24 computations (22.6% saved)

sample205.0ms (2%)

Algorithm

1×

intervals

Results

91.0ms	84×	body	2560	valid
71.0ms	118×	body	1280	valid
9.0ms	26×	body	640	valid
7.0ms	19×	body	1280	overflowed
6.0ms	297×	pre	80	true
2.0ms	1×	body	2560	invalid
2.0ms	8×	body	320	valid
2.0ms	6×	body	640	overflowed
1.0ms	2×	body	2560	overflowed
1.0ms	15×	body	80	valid
1.0ms	5×	body	320	overflowed
1.0ms	5×	body	160	valid
0.0ms	3×	body	160	overflowed
0.0ms	5×	body	80	overflowed

Compiler

Compiled 55 to 46 computations (16.4% saved)

simplify29.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5223	37

prune5.0ms (0%)

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

Merged error: 60.1b

Counts

2 → 1

Compiler

Compiled 48 to 38 computations (20.8% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
2.3b	(-.f64 (exp.f64 (*.f64 a eps)) 1)
2.5b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
3.1b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

rewrite29.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
10×	`add-log-exp_binary64` `difference-of-squares_binary64`
9×	`flip3--_binary64` `flip--_binary64`
7×	`associate-r_binary64` `associate-l_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`sub-neg_binary64` `difference-of-sqr-1_binary64` `distribute-lft-out--_binary64`
4×	`frac-times_binary64`
3×	`diff-log_binary64`
2×	`associate-r/_binary64` `associate-l/_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 81

Calls

4 calls:

11.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
7.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
4.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
4.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)

series43.0ms (0.4%)

Counts

4 → 12

Calls

4 calls:

15.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
13.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
8.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
7.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)

simplify116.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	5019	1893

prune89.0ms (0.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	87	6	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	6	94

Merged error: 49.9b

Counts

94 → 6

Compiler

Compiled 3106 to 1352 computations (56.5% saved)

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

2.5b	(+.f64 (.f64 1/6 (.f64 (pow.f64 eps 3) (pow.f64 a 3))) (.f64 eps (+.f64 a (.f64 eps (.f64 1/2 (.f64 a a))))))
3.1b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
6.0b	(.f64 eps (.f64 1/2 (*.f64 a a)))
13.2b	(*.f64 (pow.f64 eps 3) (pow.f64 a 3))

rewrite37.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64`
25×	`add-exp-log_binary64`
16×	`unswap-sqr_binary64`
15×	`add-cbrt-cube_binary64` `associate-l_binary64` `prod-exp_binary64`
14×	`*-un-lft-identity_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
13×	`pow1_binary64` `associate-r_binary64`
11×	`add-cube-cbrt_binary64`
10×	`sqr-pow_binary64`
8×	`add-log-exp_binary64`
7×	`pow-prod-down_binary64` `cbrt-unprod_binary64`
6×	`pow-to-exp_binary64` `pow-exp_binary64`
2×	`difference-of-squares_binary64` `associate-+r+_binary64` `unpow3_binary64` `*-commutative_binary64` `cube-mult_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `difference-of-sqr-1_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 108

Calls

4 calls:

10.0ms	(+.f64 (.f64 1/6 (.f64 (pow.f64 eps 3) (pow.f64 a 3))) (.f64 eps (+.f64 a (.f64 eps (.f64 1/2 (.f64 a a))))))
10.0ms	(*.f64 (pow.f64 eps 3) (pow.f64 a 3))
8.0ms	(.f64 eps (.f64 1/2 (*.f64 a a)))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

series59.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

25.0ms	(+.f64 (.f64 1/6 (.f64 (pow.f64 eps 3) (pow.f64 a 3))) (.f64 eps (+.f64 a (.f64 eps (.f64 1/2 (.f64 a a))))))
15.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
11.0ms	(*.f64 (pow.f64 eps 3) (pow.f64 a 3))
8.0ms	(.f64 eps (.f64 1/2 (*.f64 a a)))

simplify58.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5120	2087

prune162.0ms (1.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	117	3	120
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	120	6	126

Merged error: 49.7b

Counts

126 → 6

Compiler

Compiled 5565 to 2883 computations (48.2% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.1b	(.f64 eps (+.f64 a (.f64 eps (.f64 (.f64 a a) 1/2))))
2.5b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
3.1b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
6.0b	(.f64 eps (.f64 (*.f64 a a) 1/2))

rewrite26.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
15×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64`
7×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `add-cube-cbrt_binary64` `prod-exp_binary64`
6×	`associate-l_binary64`
4×	`associate-r_binary64` `difference-of-squares_binary64`
2×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `associate-r/_binary64` `difference-of-sqr-1_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `-commutative_binary64`
1×	`flip3-+_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `flip-+_binary64`

Counts

4 → 73

Calls

4 calls:

8.0ms	(.f64 eps (.f64 (*.f64 a a) 1/2))
6.0ms	(.f64 eps (+.f64 a (.f64 eps (.f64 (.f64 a a) 1/2))))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
4.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)

series44.0ms (0.4%)

Counts

4 → 12

Calls

4 calls:

14.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
14.0ms	(.f64 eps (+.f64 a (.f64 eps (.f64 (.f64 a a) 1/2))))
8.0ms	(.f64 eps (.f64 (*.f64 a a) 1/2))
7.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)

simplify65.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5237	1351

prune100.0ms (1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	79	6	85
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	82	9	91

Merged error: 49.2b

Counts

91 → 9

Compiler

Compiled 3233 to 1534 computations (52.6% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.1b	(.f64 eps (+.f64 a (.f64 eps (.f64 (.f64 a a) 1/2))))
2.5b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
3.1b	(-.f64 (exp.f64 (*.f64 eps (+.f64 a b))) 1)
6.0b	(.f64 eps (.f64 (*.f64 a a) 1/2))

rewrite26.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
15×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64`
7×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `add-cube-cbrt_binary64` `prod-exp_binary64`
6×	`associate-l_binary64`
4×	`associate-r_binary64` `difference-of-squares_binary64`
2×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `associate-r/_binary64` `difference-of-sqr-1_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `-commutative_binary64`
1×	`flip3-+_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `flip-+_binary64`

Counts

4 → 73

Calls

4 calls:

8.0ms	(.f64 eps (.f64 (*.f64 a a) 1/2))
6.0ms	(.f64 eps (+.f64 a (.f64 eps (.f64 (.f64 a a) 1/2))))
6.0ms	(-.f64 (exp.f64 (*.f64 eps (+.f64 a b))) 1)
4.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)

series42.0ms (0.4%)

Counts

4 → 12

Calls

4 calls:

14.0ms	(.f64 eps (+.f64 a (.f64 eps (.f64 (.f64 a a) 1/2))))
13.0ms	(-.f64 (exp.f64 (*.f64 eps (+.f64 a b))) 1)
9.0ms	(.f64 eps (.f64 (*.f64 a a) 1/2))
7.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)

simplify111.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4946	1339
1	4946	1339

prune81.0ms (0.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	86	8	94

Merged error: 49.2b

Counts

94 → 8

Compiler

Compiled 3176 to 1559 computations (50.9% saved)

regimes181.0ms (1.8%)

Compiler: Compiled 831 to 621 computations (25.3% saved)

bsearch116.0ms (1.1%)

Steps

Iters	Range		Point
7	9.542424670407637e+104	1.7718442551823356e+106	1.0020287718930736e+105
6	-4.455876055149492e+209	-4.345940818860064e+208	-1.8812294181881513e+209

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	80	127
1	80	127

end0.0ms (0%)

sample6.9s (67.4%)

Algorithm

1×

intervals

Results

2.7s	2564×	body	2560	valid
2.0s	3495×	body	1280	valid
326.0ms	992×	body	640	valid
263.0ms	640×	body	1280	overflowed
196.0ms	9693×	pre	80	true
110.0ms	408×	body	640	overflowed
90.0ms	143×	body	2560	overflowed
79.0ms	351×	body	320	valid
35.0ms	180×	body	320	overflowed
35.0ms	452×	body	80	valid
23.0ms	146×	body	160	valid
15.0ms	224×	body	80	overflowed
12.0ms	93×	body	160	overflowed
5.0ms	5×	body	2560	invalid

Compiler

Compiled 396 to 291 computations (26.5% saved)

Details

analyze1.6s (16%)

sample205.0ms (2%)

simplify29.0ms (0.3%)

prune5.0ms (0%)

localize15.0ms (0.2%)

rewrite29.0ms (0.3%)

series43.0ms (0.4%)

simplify116.0ms (1.1%)

prune89.0ms (0.9%)

localize28.0ms (0.3%)

rewrite37.0ms (0.4%)

series59.0ms (0.6%)

simplify58.0ms (0.6%)

prune162.0ms (1.6%)

localize21.0ms (0.2%)

rewrite26.0ms (0.3%)

series44.0ms (0.4%)

simplify65.0ms (0.6%)

prune100.0ms (1%)

localize21.0ms (0.2%)

rewrite26.0ms (0.3%)

series42.0ms (0.4%)

simplify111.0ms (1.1%)

prune81.0ms (0.8%)

regimes181.0ms (1.8%)

bsearch116.0ms (1.1%)

simplify5.0ms (0%)

end0.0ms (0%)

sample6.9s (67.4%)

Profiling