Details

analyze1.8s

Algorithm

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

sample198.0ms

Algorithm

intervals

Results

87.0ms	81×	body	2560	valid
62.0ms	105×	body	1280	valid
13.0ms	38×	body	640	valid
7.0ms	16×	body	1280	overflowed
6.0ms	298×	pre	80	true
3.0ms	15×	body	320	valid
2.0ms	7×	body	640	overflowed
2.0ms	8×	body	320	overflowed
1.0ms	7×	body	160	valid
1.0ms	1×	body	2560	overflowed
1.0ms	10×	body	80	valid
0.0ms	7×	body	80	overflowed
0.0ms	3×	body	160	overflowed

simplify28.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5218	37

prune3.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 61.5b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

1.0b	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
4.3b	(-.f64 (exp.f64 (*.f64 a eps)) 1)
4.4b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
6.1b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

rewrite28.0ms

Algorithm

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:

12.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
4.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)
4.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

series146.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
23.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)
24.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
49.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

simplify91.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4976	1893
1	4976	1893

prune92.0ms

Filtered

70 candidates to 93 candidates (-32.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	91	3	94

Merged error: 49.3b

Counts

94 → 3

localize28.0ms

Local error

Found 4 expressions with local error:

4.4b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
5.0b	(.f64 eps (.f64 1/2 (*.f64 a a)))
6.1b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
14.3b	(*.f64 (pow.f64 eps 3) (pow.f64 a 3))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64`
25×	`add-exp-log_binary64`
17×	`*-un-lft-identity_binary64`
16×	`unswap-sqr_binary64`
15×	`add-cbrt-cube_binary64` `associate-l_binary64` `prod-exp_binary64`
14×	`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`
4×	`difference-of-squares_binary64`
2×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `difference-of-sqr-1_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `unpow3_binary64` `*-commutative_binary64` `cube-mult_binary64`

Counts

4 → 110

Calls

4 calls:

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

series156.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
32.0ms	(.f64 eps (.f64 1/2 (*.f64 a a)))
49.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
48.0ms	(*.f64 (pow.f64 eps 3) (pow.f64 a 3))

simplify72.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4954	1633
1	4954	1633

prune136.0ms

Filtered

71 candidates to 122 candidates (-71.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	118	4	122
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	119	6	125

Merged error: 48.7b

Counts

125 → 6

localize28.0ms

Local error

Found 4 expressions with local error:

3.4b	(.f64 (+.f64 (.f64 1/6 (pow.f64 (.f64 eps a) 3)) (.f64 eps (+.f64 a (.f64 eps (.f64 1/2 (.f64 a a)))))) (-.f64 (exp.f64 (.f64 b eps)) 1))
4.4b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
5.0b	(.f64 eps (.f64 1/2 (*.f64 a a)))
6.1b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

13.0ms	(.f64 (+.f64 (.f64 1/6 (pow.f64 (.f64 eps a) 3)) (.f64 eps (+.f64 a (.f64 eps (.f64 1/2 (.f64 a a)))))) (-.f64 (exp.f64 (.f64 b eps)) 1))
4.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
8.0ms	(.f64 eps (.f64 1/2 (*.f64 a a)))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

series208.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(.f64 (+.f64 (.f64 1/6 (pow.f64 (.f64 eps a) 3)) (.f64 eps (+.f64 a (.f64 eps (.f64 1/2 (.f64 a a)))))) (-.f64 (exp.f64 (.f64 b eps)) 1))
24.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
33.0ms	(.f64 eps (.f64 1/2 (*.f64 a a)))
42.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

simplify84.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5000	2699

prune143.0ms

Filtered

66 candidates to 95 candidates (-43.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	90	5	95
Fresh	3	1	4
Picked	1	0	1
Done	0	1	1
Total	94	7	101

Merged error: 48.3b

Counts

101 → 7

localize29.0ms

Local error

Found 4 expressions with local error:

2.4b	(.f64 (+.f64 (.f64 1/6 (pow.f64 (.f64 eps a) 3)) (.f64 eps (+.f64 a (log.f64 (pow.f64 (sqrt.f64 (exp.f64 eps)) (.f64 a a)))))) (-.f64 (exp.f64 (.f64 b eps)) 1))
3.2b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (+.f64 (.f64 1/6 (pow.f64 (.f64 eps a) 3)) (.f64 eps (+.f64 a (log.f64 (pow.f64 (sqrt.f64 (exp.f64 eps)) (.f64 a a)))))) (-.f64 (exp.f64 (.f64 b eps)) 1)))
4.4b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
6.1b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
15×	`*-un-lft-identity_binary64`
9×	`flip3--_binary64` `flip--_binary64`
8×	`add-log-exp_binary64` `associate-/r/_binary64` `frac-times_binary64`
7×	`associate-r_binary64`
6×	`flip3-+_binary64` `pow1_binary64` `associate-*r/_binary64` `add-cube-cbrt_binary64` `difference-of-squares_binary64` `flip-+_binary64`
5×	`cbrt-unprod_binary64` `prod-exp_binary64`
4×	`sub-neg_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `associate-*l/_binary64`
3×	`difference-of-sqr-1_binary64` `associate-l_binary64` `distribute-lft-out--_binary64`
2×	`associate-/l/_binary64` `diff-log_binary64`
1×	`pow-prod-down_binary64` `associate-/r_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `times-frac_binary64` `div-inv_binary64` `*-commutative_binary64`

Counts

4 → 93

Calls

4 calls:

13.0ms	(.f64 (+.f64 (.f64 1/6 (pow.f64 (.f64 eps a) 3)) (.f64 eps (+.f64 a (log.f64 (pow.f64 (sqrt.f64 (exp.f64 eps)) (.f64 a a)))))) (-.f64 (exp.f64 (.f64 b eps)) 1))
19.0ms	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (+.f64 (.f64 1/6 (pow.f64 (.f64 eps a) 3)) (.f64 eps (+.f64 a (log.f64 (pow.f64 (sqrt.f64 (exp.f64 eps)) (.f64 a a)))))) (-.f64 (exp.f64 (.f64 b eps)) 1)))
4.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

series791.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(.f64 (+.f64 (.f64 1/6 (pow.f64 (.f64 eps a) 3)) (.f64 eps (+.f64 a (log.f64 (pow.f64 (sqrt.f64 (exp.f64 eps)) (.f64 a a)))))) (-.f64 (exp.f64 (.f64 b eps)) 1))
515.0ms	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (+.f64 (.f64 1/6 (pow.f64 (.f64 eps a) 3)) (.f64 eps (+.f64 a (log.f64 (pow.f64 (sqrt.f64 (exp.f64 eps)) (.f64 a a)))))) (-.f64 (exp.f64 (.f64 b eps)) 1)))
24.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
47.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

simplify80.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4967	4626
1	4967	4626

prune153.0ms

Filtered

80 candidates to 105 candidates (-31.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	104	1	105
Fresh	5	0	5
Picked	1	0	1
Done	0	1	1
Total	110	2	112

Merged error: 0.0b

Counts

112 → 2

regimes37.0ms

Accuracy

86.9% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 3.3b

bsearch1.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	53	133
1	53	133

end0.0ms

sample6.4s

Algorithm

intervals

Results

2.8s	2640×	body	2560	valid
1.9s	3335×	body	1280	valid
387.0ms	1115×	body	640	valid
291.0ms	662×	body	1280	overflowed
204.0ms	9695×	pre	80	true
112.0ms	173×	body	2560	overflowed
107.0ms	364×	body	640	overflowed
80.0ms	343×	body	320	valid
39.0ms	191×	body	320	overflowed
34.0ms	438×	body	80	valid
20.0ms	129×	body	160	valid
16.0ms	229×	body	80	overflowed
10.0ms	71×	body	160	overflowed
3.0ms	3×	body	2560	invalid
1.0ms	2×	body	1280	invalid

Details

analyze1.8s

sample198.0ms

simplify28.0ms

prune3.0ms

localize18.0ms

rewrite28.0ms

series146.0ms

simplify91.0ms

prune92.0ms

localize28.0ms

rewrite32.0ms

series156.0ms

simplify72.0ms

prune136.0ms

localize28.0ms

rewrite34.0ms

series208.0ms

simplify84.0ms

prune143.0ms

localize29.0ms

rewrite45.0ms

series791.0ms

simplify80.0ms

prune153.0ms

regimes37.0ms

bsearch1.0ms

simplify4.0ms

end0.0ms

sample6.4s

Profiling