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)

sample28.0ms (1%)

Algorithm

1×

intervals

Results

13.0ms	75×	body	1024	valid
4.0ms	41×	body	512	valid
3.0ms	102×	body	128	valid
2.0ms	31×	body	256	valid
1.0ms	7×	body	2048	valid

Compiler

Compiled 13 to 12 computations (7.7% saved)

simplify180.0ms (6.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

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: 39.6b

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)
4.5b	(-.f64 (exp.f64 x) 1)

rewrite19.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64_2165`
30×	`*-un-lft-identity_binary64_2143`
21×	`times-frac_binary64_2149`
15×	`add-cube-cbrt_binary64_2178`
10×	`difference-of-squares_binary64_2112`
7×	`associate-/l*_binary64_2088`
5×	`distribute-lft-out--_binary64_2095` `difference-of-sqr-1_binary64_2113`
4×	`add-log-exp_binary64_2182` `add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
3×	`associate-/r*_binary64_2087` `cancel-sign-sub-inv_binary64_2109`
2×	`pow1_binary64_2204` `flip--_binary64_2118` `flip3--_binary64_2147` `associate-/l/_binary64_2090`
1×	`cbrt-undiv_binary64_2177` `diff-log_binary64_2235` `clear-num_binary64_2142` `sub-neg_binary64_2136` `div-inv_binary64_2140` `div-exp_binary64_2194` `frac-2neg_binary64_2154` `div-sub_binary64_2148`

Counts

2 → 64

Calls

2 calls:

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

series75.0ms (2.6%)

Counts

2 → 6

Calls

2 calls:

57.0ms	(/.f64 (-.f64 (exp.f64 x) 1) x)
18.0ms	(-.f64 (exp.f64 x) 1)

simplify106.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4874	1016
1	4874	1016

prune113.0ms (4%)

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: 0.1b

Counts

71 → 3

Compiler

Compiled 1556 to 1008 computations (35.2% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite22.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_2165`
8×	`pow1_binary64_2204` `add-log-exp_binary64_2182` `add-exp-log_binary64_2181` `add-cube-cbrt_binary64_2178` `*-un-lft-identity_binary64_2143` `add-cbrt-cube_binary64_2179`
6×	`associate-r_binary64_2083` `associate-l_binary64_2084`
3×	`flip3-+_binary64_2146` `flip-+_binary64_2117`
2×	`+-commutative_binary64_2073` `distribute-rgt-in_binary64_2093` `cbrt-unprod_binary64_2176` `sum-log_binary64_2234` `pow-prod-down_binary64_2214` `prod-exp_binary64_2192` `associate-+r+_binary64_2075` `associate-r/_binary64_2085` `unswap-sqr_binary64_2111` `-commutative_binary64_2074` `distribute-lft-in_binary64_2092`

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))

series165.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

77.0ms	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
39.0ms	(+.f64 1/2 (*.f64 x 1/6))
26.0ms	(*.f64 x 1/6)
23.0ms	(+.f64 1 (.f64 x (+.f64 1/2 (.f64 x 1/6))))

simplify60.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5028	858

prune72.0ms (2.5%)

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: 0.1b

Counts

79 → 4

Compiler

Compiled 1178 to 940 computations (20.2% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 x 1/6)
10.6b	(cbrt.f64 (+.f64 1 (.f64 x (+.f64 (.f64 x 1/6) 1/2))))
10.6b	(cbrt.f64 (+.f64 1 (.f64 x (+.f64 (.f64 x 1/6) 1/2))))
10.6b	(cbrt.f64 (+.f64 1 (.f64 x (+.f64 (.f64 x 1/6) 1/2))))

rewrite22.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_2165`
9×	`cbrt-prod_binary64_2174` `add-cube-cbrt_binary64_2178` `*-un-lft-identity_binary64_2143`
6×	`pow1_binary64_2204` `add-exp-log_binary64_2181` `cbrt-div_binary64_2175` `add-cbrt-cube_binary64_2179`
4×	`add-log-exp_binary64_2182`
3×	`associate-r_binary64_2083` `associate-l_binary64_2084` `flip3-+_binary64_2146` `flip-+_binary64_2117` `pow1/3_binary64_2225`
1×	`cbrt-unprod_binary64_2176` `pow-prod-down_binary64_2214` `prod-exp_binary64_2192` `unswap-sqr_binary64_2111` `*-commutative_binary64_2074`

Counts

4 → 57

Calls

4 calls:

5.0ms	(cbrt.f64 (+.f64 1 (.f64 x (+.f64 (.f64 x 1/6) 1/2))))
4.0ms	(*.f64 x 1/6)
3.0ms	(cbrt.f64 (+.f64 1 (.f64 x (+.f64 (.f64 x 1/6) 1/2))))
3.0ms	(cbrt.f64 (+.f64 1 (.f64 x (+.f64 (.f64 x 1/6) 1/2))))

series198.0ms (7%)

Counts

4 → 12

Calls

4 calls:

61.0ms	(cbrt.f64 (+.f64 1 (.f64 x (+.f64 (.f64 x 1/6) 1/2))))
60.0ms	(cbrt.f64 (+.f64 1 (.f64 x (+.f64 (.f64 x 1/6) 1/2))))
56.0ms	(cbrt.f64 (+.f64 1 (.f64 x (+.f64 (.f64 x 1/6) 1/2))))
21.0ms	(*.f64 x 1/6)

simplify92.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4783	1390
1	4783	1390

prune157.0ms (5.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	70	3	73

Merged error: 0.1b

Counts

73 → 3

Compiler

Compiled 3009 to 2452 computations (18.5% saved)

localize19.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 x 1/6)
0.4b	(*.f64 x 1/36)
10.6b	(cbrt.f64 (+.f64 1 (.f64 x (+.f64 (.f64 x 1/6) 1/2))))
10.6b	(cbrt.f64 (+.f64 1 (.f64 x (+.f64 (.f64 x 1/6) 1/2))))

rewrite21.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_2165`
10×	`add-cube-cbrt_binary64_2178` `*-un-lft-identity_binary64_2143`
8×	`pow1_binary64_2204` `add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
6×	`cbrt-prod_binary64_2174` `associate-r_binary64_2083` `associate-l_binary64_2084`
4×	`add-log-exp_binary64_2182` `cbrt-div_binary64_2175`
2×	`cbrt-unprod_binary64_2176` `pow-prod-down_binary64_2214` `prod-exp_binary64_2192` `unswap-sqr_binary64_2111` `flip3-+_binary64_2146` `flip-+_binary64_2117` `*-commutative_binary64_2074` `pow1/3_binary64_2225`

Counts

4 → 62

Calls

4 calls:

4.0ms	(*.f64 x 1/6)
4.0ms	(*.f64 x 1/36)
3.0ms	(cbrt.f64 (+.f64 1 (.f64 x (+.f64 (.f64 x 1/6) 1/2))))
3.0ms	(cbrt.f64 (+.f64 1 (.f64 x (+.f64 (.f64 x 1/6) 1/2))))

series164.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

61.0ms	(cbrt.f64 (+.f64 1 (.f64 x (+.f64 (.f64 x 1/6) 1/2))))
60.0ms	(cbrt.f64 (+.f64 1 (.f64 x (+.f64 (.f64 x 1/6) 1/2))))
22.0ms	(*.f64 x 1/6)
21.0ms	(*.f64 x 1/36)

simplify91.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4835	1094
1	4835	1094

prune163.0ms (5.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	74	3	77

Merged error: 0.1b

Counts

77 → 3

Compiler

Compiled 3126 to 2535 computations (18.9% saved)

regimes17.0ms (0.6%)

Compiler: Compiled 49 to 41 computations (16.3% saved)

bsearch13.0ms (0.5%)

Steps

Iters	Range		Point
7	-0.007204926118897057	-0.00011039998681144499	-0.00018219254954158785

Compiler

Compiled 1 to 1 computations (0% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	31
1	42	31

end0.0ms (0%)

sample1.0s (35.9%)

Algorithm

1×

intervals

Results

460.0ms	2683×	body	1024	valid
128.0ms	1304×	body	512	valid
86.0ms	3077×	body	128	valid
55.0ms	270×	body	2048	valid
44.0ms	666×	body	256	valid

Compiler

Compiled 97 to 77 computations (20.6% saved)

Details

analyze4.0ms (0.1%)

sample28.0ms (1%)

simplify180.0ms (6.3%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

rewrite19.0ms (0.7%)

series75.0ms (2.6%)

simplify106.0ms (3.7%)

prune113.0ms (4%)

localize6.0ms (0.2%)

rewrite22.0ms (0.8%)

series165.0ms (5.8%)

simplify60.0ms (2.1%)

prune72.0ms (2.5%)

localize11.0ms (0.4%)

rewrite22.0ms (0.8%)

series198.0ms (7%)

simplify92.0ms (3.2%)

prune157.0ms (5.5%)

localize19.0ms (0.7%)

rewrite21.0ms (0.7%)

series164.0ms (5.8%)

simplify91.0ms (3.2%)

prune163.0ms (5.7%)

regimes17.0ms (0.6%)

bsearch13.0ms (0.5%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.0s (35.9%)

Profiling