Details

analyze1.2s

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0.1%	99.9%	0%	14

sample237.0ms

Algorithm

intervals

Results

138.0ms	46×	body	2560	valid
63.0ms	96×	body	1280	valid
18.0ms	61×	body	640	valid
4.0ms	22×	body	320	valid
2.0ms	15×	body	160	valid
1.0ms	16×	body	80	valid

simplify483.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	1004	9
1	1004	9

prune4.0ms

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

Merged error: 33.7b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
2.2b	(-.f64 x (sin.f64 x))
2.2b	(-.f64 x (tan.f64 x))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
15×	`add-cube-cbrt_binary64`
14×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
7×	`add-log-exp_binary64`
5×	`associate-/r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`pow1_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `associate-/r/_binary64`
1×	`cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

3 → 78

Calls

3 calls:

19.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
4.0ms	(-.f64 x (sin.f64 x))
6.0ms	(-.f64 x (tan.f64 x))

series42.0ms

Counts

3 → 9

Calls

3 calls:

14.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
5.0ms	(-.f64 x (sin.f64 x))
23.0ms	(-.f64 x (tan.f64 x))

simplify42.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4932	1139
1	4932	1139

prune85.0ms

Filtered

63 candidates to 87 candidates (-38.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	82	5	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	5	88

Merged error: 0.1b

Counts

88 → 5

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(*.f64 27/2800 (pow.f64 x 4))
0.1b	(.f64 (.f64 x x) 9/40)
15.1b	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 (*.f64 27/2800 (pow.f64 x 4)) 1/2))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-exp-log_binary64` `add-sqr-sqrt_binary64`
10×	`associate-r_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `pow1_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`prod-exp_binary64`
4×	`cbrt-unprod_binary64` `associate-l_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64`
3×	`pow-prod-down_binary64`
2×	`diff-log_binary64` `sqr-pow_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `associate--r+_binary64` `flip3--_binary64` `flip--_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

3 → 57

Calls

3 calls:

6.0ms	(*.f64 27/2800 (pow.f64 x 4))
6.0ms	(.f64 (.f64 x x) 9/40)
10.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 (*.f64 27/2800 (pow.f64 x 4)) 1/2))

series18.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(*.f64 27/2800 (pow.f64 x 4))
4.0ms	(.f64 (.f64 x x) 9/40)
7.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 (*.f64 27/2800 (pow.f64 x 4)) 1/2))

simplify28.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	4961	578
1	4961	578

prune59.0ms

Filtered

40 candidates to 66 candidates (-65.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	66	5	71

Merged error: 0.1b

Counts

71 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))))
0.0b	(log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
2.2b	(-.f64 x (sin.f64 x))
2.2b	(-.f64 x (tan.f64 x))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

71×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
62×	`exp-prod_binary64`
50×	`times-frac_binary64`
32×	`log-pow_binary64`
27×	`add-cube-cbrt_binary64`
22×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
9×	`add-log-exp_binary64`
5×	`pow1_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/r/_binary64` `flip--_binary64`
3×	`log-prod_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `exp-diff_binary64` `div-sub_binary64` `div-inv_binary64`
1×	`rem-log-exp_binary64` `rem-exp-log_binary64` `log-div_binary64`

Counts

4 → 110

Calls

4 calls:

11.0ms	(exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))))
14.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
4.0ms	(-.f64 x (sin.f64 x))
4.0ms	(-.f64 x (tan.f64 x))

series52.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))))
15.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
5.0ms	(-.f64 x (sin.f64 x))
10.0ms	(-.f64 x (tan.f64 x))

simplify51.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5161	1379

prune91.0ms

Filtered

87 candidates to 122 candidates (-40.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	119	3	122
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	122	5	127

Merged error: 0.0b

Counts

127 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
2.2b	(-.f64 x (tan.f64 x))
2.2b	(-.f64 x (tan.f64 x))
2.3b	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity_binary64`
44×	`add-sqr-sqrt_binary64`
33×	`times-frac_binary64`
18×	`distribute-lft-out--_binary64`
16×	`add-cube-cbrt_binary64`
12×	`difference-of-squares_binary64`
10×	`add-log-exp_binary64`
6×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/r/_binary64` `flip--_binary64`
5×	`associate-/r*_binary64`
4×	`pow1_binary64`
3×	`sub-neg_binary64` `diff-log_binary64` `distribute-rgt-out--_binary64` `associate-/l*_binary64` `div-inv_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `sub-div_binary64` `frac-sub_binary64`

Counts

4 → 91

Calls

4 calls:

7.0ms	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
4.0ms	(-.f64 x (tan.f64 x))
4.0ms	(-.f64 x (tan.f64 x))
31.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))

series65.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
13.0ms	(-.f64 x (tan.f64 x))
11.0ms	(-.f64 x (tan.f64 x))
29.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))

simplify45.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5167	1430

prune74.0ms

Filtered

80 candidates to 103 candidates (-28.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	101	2	103
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	104	4	108

Merged error: 0.0b

Counts

108 → 4

regimes45.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.3b

bsearch47.0ms

Steps

Iters	Range		Point
10	4.6803344332587176e-14	0.1717659009207132	0.02727798752832581
9	-0.03849650220869293	-9.559634869391715e-10	-0.029873394671195968

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	102	65
1	102	65

end0.0ms

sample6.7s

Algorithm

intervals

Results

4.1s	1586×	body	2560	valid
1.6s	2669×	body	1280	valid
545.0ms	1991×	body	640	valid
171.0ms	936×	body	320	valid
63.0ms	481×	body	160	valid
26.0ms	337×	body	80	valid

Details

analyze1.2s

sample237.0ms

simplify483.0ms

prune4.0ms

localize10.0ms

rewrite33.0ms

series42.0ms

simplify42.0ms

prune85.0ms

localize9.0ms

rewrite23.0ms

series18.0ms

simplify28.0ms

prune59.0ms

localize11.0ms

rewrite38.0ms

series52.0ms

simplify51.0ms

prune91.0ms

localize9.0ms

rewrite49.0ms

series65.0ms

simplify45.0ms

prune74.0ms

regimes45.0ms

bsearch47.0ms

simplify3.0ms

end0.0ms

sample6.7s

Profiling