Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
62.5%	25%	12.5%	4
68.7%	12.5%	18.8%	5
71.8%	6.2%	21.9%	6
73.4%	3.1%	23.5%	7
74.2%	1.6%	24.3%	8
74.6%	0.8%	24.6%	9
75%	0.4%	24.6%	10
75.1%	0.2%	24.7%	11
75.1%	0.1%	24.8%	12
75.1%	0%	24.8%	13
75.2%	0%	24.8%	14

Compiler

Compiled 7 to 6 computations (14.3% saved)

sample30.0ms (1.1%)

Algorithm

1×

intervals

Results

14.0ms	77×	body	1024	valid
5.0ms	47×	body	512	valid
3.0ms	106×	body	128	valid
2.0ms	11×	body	2048	valid
1.0ms	15×	body	256	valid

Compiler

Compiled 13 to 12 computations (7.7% saved)

simplify177.0ms (6.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	166	9
1	166	9

prune2.0ms (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

Merged error: 37.8b

Counts

2 → 1

Compiler

Compiled 12 to 10 computations (16.7% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 (exp.f64 x) 1) x)
3.0b	(-.f64 (exp.f64 x) 1)

rewrite18.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64_2828`
30×	`*-un-lft-identity_binary64_2806`
21×	`times-frac_binary64_2812`
15×	`add-cube-cbrt_binary64_2841`
10×	`difference-of-squares_binary64_2775`
7×	`associate-/l*_binary64_2751`
5×	`distribute-lft-out--_binary64_2758` `difference-of-sqr-1_binary64_2776`
4×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `add-log-exp_binary64_2845`
3×	`cancel-sign-sub-inv_binary64_2772` `associate-/r*_binary64_2750`
2×	`associate-/l/_binary64_2753` `flip3--_binary64_2810` `flip--_binary64_2781` `pow1_binary64_2867`
1×	`div-inv_binary64_2803` `div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `div-sub_binary64_2811` `diff-log_binary64_2898` `sub-neg_binary64_2799` `clear-num_binary64_2805` `frac-2neg_binary64_2817`

Counts

2 → 64

Calls

2 calls:

8.0ms	(/.f64 (-.f64 (exp.f64 x) 1) x)
5.0ms	(-.f64 (exp.f64 x) 1)

series67.0ms (2.5%)

Counts

2 → 6

Calls

2 calls:

49.0ms	(/.f64 (-.f64 (exp.f64 x) 1) x)
18.0ms	(-.f64 (exp.f64 x) 1)

simplify109.0ms (4%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4874	1016
1	4874	1016

prune62.0ms (2.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	3	71

Merged error: 0.0b

Counts

71 → 3

Compiler

Compiled 888 to 487 computations (45.2% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (.f64 x (+.f64 1/2 (.f64 x 1/6))))
0.0b	(+.f64 1/2 (*.f64 x 1/6))
0.1b	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
0.3b	(*.f64 x 1/6)

rewrite21.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_2828`
8×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `*-un-lft-identity_binary64_2806` `add-log-exp_binary64_2845` `add-cube-cbrt_binary64_2841` `pow1_binary64_2867`
6×	`associate-l_binary64_2747` `associate-r_binary64_2746`
3×	`flip-+_binary64_2780` `flip3-+_binary64_2809`
2×	`-commutative_binary64_2737` `distribute-lft-in_binary64_2755` `associate-+r+_binary64_2738` `distribute-rgt-in_binary64_2756` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `sum-log_binary64_2897` `associate-r/_binary64_2748` `pow-prod-down_binary64_2877` `unswap-sqr_binary64_2774` `+-commutative_binary64_2736`

Counts

4 → 64

Calls

4 calls:

6.0ms	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
4.0ms	(*.f64 x 1/6)
4.0ms	(+.f64 1 (.f64 x (+.f64 1/2 (.f64 x 1/6))))
3.0ms	(+.f64 1/2 (*.f64 x 1/6))

series163.0ms (6.1%)

Counts

4 → 12

Calls

4 calls:

74.0ms	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
43.0ms	(+.f64 1/2 (*.f64 x 1/6))
23.0ms	(*.f64 x 1/6)
22.0ms	(+.f64 1 (.f64 x (+.f64 1/2 (.f64 x 1/6))))

simplify60.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5028	858

prune64.0ms (2.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	75	4	79

Merged error: 0.0b

Counts

79 → 4

Compiler

Compiled 1069 to 844 computations (21% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (+.f64 1 (.f64 x 1/2)) (.f64 (*.f64 x 1/6) x))
0.1b	(.f64 (.f64 x 1/6) x)
0.3b	(*.f64 x 1/6)

rewrite19.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `pow1_binary64_2867`
8×	`add-sqr-sqrt_binary64_2828` `add-log-exp_binary64_2845`
6×	`-un-lft-identity_binary64_2806` `add-cube-cbrt_binary64_2841` `associate-r*_binary64_2746`
4×	`associate-l_binary64_2747` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `pow-prod-down_binary64_2877`
3×	`sum-log_binary64_2897`
2×	`*-commutative_binary64_2737`
1×	`associate-+l+_binary64_2739` `flip-+_binary64_2780` `flip3-+_binary64_2809` `unswap-sqr_binary64_2774` `+-commutative_binary64_2736`

Counts

3 → 49

Calls

3 calls:

6.0ms	(+.f64 (+.f64 1 (.f64 x 1/2)) (.f64 (*.f64 x 1/6) x))
5.0ms	(.f64 (.f64 x 1/6) x)
4.0ms	(*.f64 x 1/6)

series87.0ms (3.2%)

Counts

3 → 9

Calls

3 calls:

34.0ms	(.f64 (.f64 x 1/6) x)
28.0ms	(+.f64 (+.f64 1 (.f64 x 1/2)) (.f64 (*.f64 x 1/6) x))
25.0ms	(*.f64 x 1/6)

simplify75.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4917	588
1	4917	588

prune49.0ms (1.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	58	0	58
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	58	4	62

Merged error: 0.0b

Counts

62 → 4

Compiler

Compiled 857 to 654 computations (23.7% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (exp.f64 x) 1)
0.0b	(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1))
0.0b	(pow.f64 (exp.f64 x) 2)
3.0b	(+.f64 (pow.f64 (exp.f64 x) 2) -1)

rewrite37.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`*-un-lft-identity_binary64_2806`
33×	`add-sqr-sqrt_binary64_2828`
32×	`times-frac_binary64_2812`
24×	`difference-of-sqr--1_binary64_2777`
21×	`add-cube-cbrt_binary64_2841`
16×	`distribute-lft-out_binary64_2757`
9×	`unpow-prod-down_binary64_2885`
8×	`add-log-exp_binary64_2845` `associate-/l*_binary64_2751`
7×	`sqr-pow_binary64_2778` `unpow2_binary64_2871`
6×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
5×	`pow1_binary64_2867`
4×	`associate-/r*_binary64_2750` `pow-pow_binary64_2878` `flip-+_binary64_2780` `flip3-+_binary64_2809`
3×	`exp-prod_binary64_2858` `pow-unpow_binary64_2883`
2×	`associate-/l/_binary64_2753` `sum-log_binary64_2897` `associate-/r/_binary64_2752` `+-commutative_binary64_2736`
1×	`pow-exp_binary64_2874` `div-inv_binary64_2803` `div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `pow-to-exp_binary64_2875` `clear-num_binary64_2805` `frac-2neg_binary64_2817`

Counts

4 → 109

Calls

4 calls:

13.0ms	(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1))
6.0ms	(+.f64 (pow.f64 (exp.f64 x) 2) -1)
4.0ms	(+.f64 (exp.f64 x) 1)
4.0ms	(pow.f64 (exp.f64 x) 2)

series163.0ms (6%)

Counts

4 → 12

Calls

4 calls:

97.0ms	(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1))
33.0ms	(+.f64 (pow.f64 (exp.f64 x) 2) -1)
22.0ms	(pow.f64 (exp.f64 x) 2)
11.0ms	(+.f64 (exp.f64 x) 1)

simplify85.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4977	1939
1	4977	1939

prune107.0ms (4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	1	0	1
Picked	1	0	1
Done	0	2	2
Total	122	3	125

Merged error: 0.0b

Counts

125 → 3

Compiler

Compiled 2162 to 1369 computations (36.7% saved)

regimes71.0ms (2.7%)

Compiler: Compiled 458 to 368 computations (19.7% saved)

bsearch1.0ms (0%)

Compiler: Compiled 6 to 5 computations (16.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	47
1	31	47

end0.0ms (0%)

sample1.2s (44.2%)

Algorithm

1×

intervals

Results

451.0ms	2629×	body	1024	valid
125.0ms	1283×	body	512	valid
85.0ms	3122×	body	128	valid
50.0ms	702×	body	256	valid
49.0ms	264×	body	2048	valid

Compiler

Compiled 269 to 212 computations (21.2% saved)

Details

analyze4.0ms (0.1%)

sample30.0ms (1.1%)

simplify177.0ms (6.6%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

rewrite18.0ms (0.7%)

series67.0ms (2.5%)

simplify109.0ms (4%)

prune62.0ms (2.3%)

localize6.0ms (0.2%)

rewrite21.0ms (0.8%)

series163.0ms (6.1%)

simplify60.0ms (2.2%)

prune64.0ms (2.4%)

localize7.0ms (0.2%)

rewrite19.0ms (0.7%)

series87.0ms (3.2%)

simplify75.0ms (2.8%)

prune49.0ms (1.8%)

localize8.0ms (0.3%)

rewrite37.0ms (1.4%)

series163.0ms (6%)

simplify85.0ms (3.2%)

prune107.0ms (4%)

regimes71.0ms (2.7%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.2s (44.2%)

Profiling