Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1

Compiler

Compiled 22 to 17 computations (22.7% saved)

sample18.0ms (0.5%)

Algorithm

1×

intervals

Results

7.0ms	256×	pre	128	true
6.0ms	256×	body	128	valid

Compiler

Compiled 29 to 25 computations (13.8% saved)

simplify223.0ms (6.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	472	10
1	472	10

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: 8.3b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.0b	(/.f64 x0 (-.f64 1 x1))
7.4b	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)

rewrite25.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64_2487`
28×	`*-un-lft-identity_binary64_2465`
19×	`times-frac_binary64_2471`
14×	`add-cube-cbrt_binary64_2500`
10×	`difference-of-squares_binary64_2434`
6×	`associate-/r*_binary64_2409`
5×	`distribute-lft-out--_binary64_2417`
4×	`add-log-exp_binary64_2504` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
3×	`cancel-sign-sub-inv_binary64_2431` `associate-/l*_binary64_2410`
2×	`flip--_binary64_2440` `pow1_binary64_2526` `associate-/r/_binary64_2411` `flip3--_binary64_2469`
1×	`clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `sub-neg_binary64_2458` `div-exp_binary64_2516` `div-inv_binary64_2462` `diff-log_binary64_2557` `frac-2neg_binary64_2476`

Counts

2 → 58

Calls

2 calls:

15.0ms	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)
6.0ms	(/.f64 x0 (-.f64 1 x1))

series127.0ms (3.5%)

Counts

2 → 6

Calls

2 calls:

73.0ms	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)
54.0ms	(/.f64 x0 (-.f64 1 x1))

simplify53.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4939	940
1	4939	940

prune49.0ms (1.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	62	2	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	2	65

Merged error: 6.7b

Counts

65 → 2

Compiler

Compiled 896 to 538 computations (40% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (-.f64 1 x1) (-.f64 1 x1))
0.5b	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
1.0b	(/.f64 x0 (-.f64 1 x1))
5.9b	(-.f64 (/.f64 x0 (*.f64 (-.f64 1 x1) (-.f64 1 x1))) x0)

rewrite64.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64_2465`
52×	`add-sqr-sqrt_binary64_2487`
22×	`add-cube-cbrt_binary64_2500`
19×	`times-frac_binary64_2471`
18×	`difference-of-squares_binary64_2434`
11×	`distribute-lft-out--_binary64_2417` `pow1_binary64_2526`
9×	`cancel-sign-sub-inv_binary64_2431`
8×	`add-log-exp_binary64_2504` `flip--_binary64_2440` `swap-sqr_binary64_2432` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `flip3--_binary64_2469`
6×	`associate-/r_binary64_2409` `associate-r_binary64_2405` `associate-l*_binary64_2406`
4×	`distribute-lft-in_binary64_2414` `frac-times_binary64_2475` `distribute-rgt-in_binary64_2415`
3×	`sub-neg_binary64_2458` `associate-/l*_binary64_2410`
2×	`associate-l/_binary64_2408` `associate-r/_binary64_2407` `associate-/r/_binary64_2411`
1×	`flip3-+_binary64_2468` `*-commutative_binary64_2396` `+-commutative_binary64_2395` `pow-plus_binary64_2528` `sum-log_binary64_2556` `flip-+_binary64_2439` `clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `unswap-sqr_binary64_2433` `div-exp_binary64_2516` `div-inv_binary64_2462` `diff-log_binary64_2557` `pow2_binary64_2546` `prod-exp_binary64_2514` `frac-2neg_binary64_2476` `pow-prod-down_binary64_2536` `distribute-lft-out_binary64_2416` `pow-sqr_binary64_2438` `pow-prod-up_binary64_2535` `cbrt-unprod_binary64_2498`

Counts

4 → 122

Calls

4 calls:

18.0ms	(-.f64 (/.f64 x0 (*.f64 (-.f64 1 x1) (-.f64 1 x1))) x0)
15.0ms	(*.f64 (-.f64 1 x1) (-.f64 1 x1))
11.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
6.0ms	(/.f64 x0 (-.f64 1 x1))

series256.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

123.0ms	(-.f64 (/.f64 x0 (*.f64 (-.f64 1 x1) (-.f64 1 x1))) x0)
67.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
50.0ms	(/.f64 x0 (-.f64 1 x1))
16.0ms	(*.f64 (-.f64 1 x1) (-.f64 1 x1))

simplify62.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5082	1914

prune160.0ms (4.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	132	2	134
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	134	2	136

Merged error: 5.2b

Counts

136 → 2

Compiler

Compiled 3610 to 2238 computations (38% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 x1 (+.f64 x1 -2))
0.5b	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
1.0b	(/.f64 x0 (-.f64 1 x1))
5.9b	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)

rewrite48.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64_2487`
36×	`*-un-lft-identity_binary64_2465`
19×	`times-frac_binary64_2471`
18×	`add-cube-cbrt_binary64_2500`
10×	`difference-of-squares_binary64_2434`
8×	`add-log-exp_binary64_2504` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
6×	`associate-/r*_binary64_2409` `pow1_binary64_2526`
5×	`distribute-lft-out--_binary64_2417`
4×	`associate-r_binary64_2405`
3×	`cancel-sign-sub-inv_binary64_2431` `associate-/l_binary64_2410` `associate-l*_binary64_2406`
2×	`flip3-+_binary64_2468` `flip--_binary64_2440` `flip-+_binary64_2439` `associate-*r/_binary64_2407` `associate-/r/_binary64_2411` `distribute-lft-out_binary64_2416` `flip3--_binary64_2469`
1×	`distribute-lft-in_binary64_2414` `*-commutative_binary64_2396` `+-commutative_binary64_2395` `sum-log_binary64_2556` `clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `sub-neg_binary64_2458` `unswap-sqr_binary64_2433` `distribute-rgt-in_binary64_2415` `div-exp_binary64_2516` `div-inv_binary64_2462` `diff-log_binary64_2557` `prod-exp_binary64_2514` `frac-2neg_binary64_2476` `pow-prod-down_binary64_2536` `cbrt-unprod_binary64_2498`

Counts

4 → 93

Calls

4 calls:

12.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
11.0ms	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)
7.0ms	(*.f64 x1 (+.f64 x1 -2))
6.0ms	(/.f64 x0 (-.f64 1 x1))

series288.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

130.0ms	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)
58.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
50.0ms	(/.f64 x0 (-.f64 1 x1))
50.0ms	(*.f64 x1 (+.f64 x1 -2))

simplify67.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5413	1541

prune123.0ms (3.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	105	2	107

Merged error: 4.3b

Counts

107 → 2

Compiler

Compiled 2924 to 1828 computations (37.5% saved)

localize17.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.5b	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
1.0b	(/.f64 x0 (-.f64 1 x1))
4.8b	(log.f64 (exp.f64 (-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)))
5.9b	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)

rewrite50.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64_2487`
37×	`*-un-lft-identity_binary64_2465`
20×	`times-frac_binary64_2471`
19×	`add-cube-cbrt_binary64_2500`
12×	`difference-of-squares_binary64_2434`
8×	`add-log-exp_binary64_2504`
7×	`log-prod_binary64_2551` `log-pow_binary64_2554`
6×	`associate-/r*_binary64_2409` `add-exp-log_binary64_2503` `distribute-lft-out--_binary64_2417` `add-cbrt-cube_binary64_2501` `cancel-sign-sub-inv_binary64_2431` `exp-prod_binary64_2517`
5×	`pow1_binary64_2526`
4×	`exp-sum_binary64_2511`
3×	`associate-/l*_binary64_2410`
2×	`flip--_binary64_2440` `sub-neg_binary64_2458` `associate-/r/_binary64_2411` `flip3--_binary64_2469`
1×	`flip3-+_binary64_2468` `log-div_binary64_2552` `+-commutative_binary64_2395` `sum-log_binary64_2556` `flip-+_binary64_2439` `clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `div-exp_binary64_2516` `div-inv_binary64_2462` `diff-log_binary64_2557` `frac-2neg_binary64_2476` `distribute-lft-out_binary64_2416` `rem-log-exp_binary64_2506` `exp-diff_binary64_2513`

Counts

4 → 93

Calls

4 calls:

12.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)))
11.0ms	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)
11.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
6.0ms	(/.f64 x0 (-.f64 1 x1))

series589.0ms (16.5%)

Counts

4 → 12

Calls

4 calls:

324.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)))
152.0ms	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)
57.0ms	(/.f64 x0 (-.f64 1 x1))
56.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))

simplify49.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5117	1819

prune138.0ms (3.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	105	2	107

Merged error: 3.2b

Counts

107 → 2

Compiler

Compiled 3093 to 1993 computations (35.6% saved)

regimes156.0ms (4.4%)

Compiler: Compiled 2104 to 1562 computations (25.8% saved)

bsearch1.0ms (0%)

Compiler: Compiled 3 to 4 computations (-33.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	58	111
1	58	111

end0.0ms (0%)

sample978.0ms (27.3%)

Algorithm

1×

intervals

Results

235.0ms	8000×	pre	128	true
184.0ms	8000×	body	128	valid

Compiler

Compiled 553 to 409 computations (26% saved)

Details

analyze3.0ms (0.1%)

sample18.0ms (0.5%)

simplify223.0ms (6.2%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

rewrite25.0ms (0.7%)

series127.0ms (3.5%)

simplify53.0ms (1.5%)

prune49.0ms (1.4%)

localize10.0ms (0.3%)

rewrite64.0ms (1.8%)

series256.0ms (7.2%)

simplify62.0ms (1.7%)

prune160.0ms (4.5%)

localize12.0ms (0.3%)

rewrite48.0ms (1.3%)

series288.0ms (8.1%)

simplify67.0ms (1.9%)

prune123.0ms (3.4%)

localize17.0ms (0.5%)

rewrite50.0ms (1.4%)

series589.0ms (16.5%)

simplify49.0ms (1.4%)

prune138.0ms (3.8%)

regimes156.0ms (4.4%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample978.0ms (27.3%)

Profiling