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 (0.6%)

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)

simplify198.0ms (6.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (39.0ms)

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: 8.2b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

1.0b	(/.f64 x0 (-.f64 1 x1))
7.3b	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)

rewrite24.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_2457`
27×	`*-un-lft-identity_binary64_2436`
19×	`times-frac_binary64_2442`
13×	`add-cube-cbrt_binary64_2468`
10×	`difference-of-squares_binary64_2405`
6×	`associate-/r*_binary64_2382`
5×	`distribute-lft-out--_binary64_2390`
4×	`add-log-exp_binary64_2472` `add-exp-log_binary64_2471` `add-cbrt-cube_binary64_2469`
3×	`associate-/l*_binary64_2383`
2×	`associate-/r/_binary64_2384` `flip3--_binary64_2440` `pow1_binary64_2494` `flip--_binary64_2411`
1×	`cbrt-undiv_binary64_2467` `div-inv_binary64_2433` `diff-log_binary64_2525` `div-exp_binary64_2484` `clear-num_binary64_2435` `frac-2neg_binary64_2447` `sub-neg_binary64_2429`

Counts

2 → 55

Calls

2 calls:

14.0ms	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)
6.0ms	(/.f64 x0 (-.f64 1 x1))

series124.0ms (4%)

Counts

2 → 6

Calls

2 calls:

64.0ms	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)
59.0ms	(/.f64 x0 (-.f64 1 x1))

simplify62.0ms (2%)

Algorithm

1×	egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5127	928

prune46.0ms (1.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	59	2	61
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	2	62

Merged error: 6.6b

Counts

62 → 2

Compiler

Compiled 870 to 523 computations (39.9% saved)

localize12.0ms (0.4%)

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))
5.8b	(-.f64 (/.f64 x0 (*.f64 (-.f64 1 x1) (-.f64 1 x1))) x0)

rewrite56.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`*-un-lft-identity_binary64_2436`
49×	`add-sqr-sqrt_binary64_2457`
19×	`add-cube-cbrt_binary64_2468` `times-frac_binary64_2442`
18×	`difference-of-squares_binary64_2405`
11×	`distribute-lft-out--_binary64_2390` `pow1_binary64_2494`
8×	`add-log-exp_binary64_2472` `swap-sqr_binary64_2403` `flip3--_binary64_2440` `add-exp-log_binary64_2471` `add-cbrt-cube_binary64_2469` `flip--_binary64_2411`
6×	`associate-/r_binary64_2382` `associate-r_binary64_2378` `associate-l*_binary64_2379`
4×	`frac-times_binary64_2446`
3×	`associate-/l*_binary64_2383` `sub-neg_binary64_2429`
2×	`associate-/r/_binary64_2384` `associate-r/_binary64_2380` `associate-l/_binary64_2381`
1×	`flip3-+_binary64_2439` `distribute-lft-out_binary64_2389` `prod-exp_binary64_2482` `cbrt-undiv_binary64_2467` `flip-+_binary64_2410` `distribute-rgt-in_binary64_2388` `*-commutative_binary64_2369` `div-inv_binary64_2433` `diff-log_binary64_2525` `pow2_binary64_2514` `pow-prod-down_binary64_2504` `div-exp_binary64_2484` `sum-log_binary64_2524` `cbrt-unprod_binary64_2466` `unswap-sqr_binary64_2404` `clear-num_binary64_2435` `pow-prod-up_binary64_2503` `+-commutative_binary64_2368` `frac-2neg_binary64_2447` `pow-plus_binary64_2496` `distribute-lft-in_binary64_2387` `pow-sqr_binary64_2409`

Counts

4 → 113

Calls

4 calls:

16.0ms	(-.f64 (/.f64 x0 (*.f64 (-.f64 1 x1) (-.f64 1 x1))) x0)
12.0ms	(*.f64 (-.f64 1 x1) (-.f64 1 x1))
11.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
6.0ms	(/.f64 x0 (-.f64 1 x1))

series258.0ms (8.3%)

Counts

4 → 12

Calls

4 calls:

126.0ms	(-.f64 (/.f64 x0 (*.f64 (-.f64 1 x1) (-.f64 1 x1))) x0)
59.0ms	(/.f64 x0 (-.f64 1 x1))
58.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
16.0ms	(*.f64 (-.f64 1 x1) (-.f64 1 x1))

simplify78.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5172	1762

prune149.0ms (4.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	123	2	125
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	125	2	127

Merged error: 5.1b

Counts

127 → 2

Compiler

Compiled 3364 to 2096 computations (37.7% saved)

localize12.0ms (0.4%)

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))
5.8b	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)

rewrite44.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64_2457`
35×	`*-un-lft-identity_binary64_2436`
19×	`times-frac_binary64_2442`
17×	`add-cube-cbrt_binary64_2468`
10×	`difference-of-squares_binary64_2405`
8×	`add-log-exp_binary64_2472` `add-exp-log_binary64_2471` `add-cbrt-cube_binary64_2469`
6×	`associate-/r*_binary64_2382` `pow1_binary64_2494`
5×	`distribute-lft-out--_binary64_2390`
4×	`associate-r_binary64_2378`
3×	`associate-/l_binary64_2383` `associate-l*_binary64_2379`
2×	`flip3-+_binary64_2439` `distribute-lft-out_binary64_2389` `flip-+_binary64_2410` `associate-/r/_binary64_2384` `flip3--_binary64_2440` `associate-*r/_binary64_2380` `flip--_binary64_2411`
1×	`prod-exp_binary64_2482` `cbrt-undiv_binary64_2467` `distribute-rgt-in_binary64_2388` `*-commutative_binary64_2369` `div-inv_binary64_2433` `diff-log_binary64_2525` `pow-prod-down_binary64_2504` `div-exp_binary64_2484` `sum-log_binary64_2524` `cbrt-unprod_binary64_2466` `unswap-sqr_binary64_2404` `clear-num_binary64_2435` `+-commutative_binary64_2368` `frac-2neg_binary64_2447` `distribute-lft-in_binary64_2387` `sub-neg_binary64_2429`

Counts

4 → 90

Calls

4 calls:

11.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
10.0ms	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)
8.0ms	(/.f64 x0 (-.f64 1 x1))
6.0ms	(*.f64 x1 (+.f64 x1 -2))

series305.0ms (9.8%)

Counts

4 → 12

Calls

4 calls:

143.0ms	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)
56.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
54.0ms	(/.f64 x0 (-.f64 1 x1))
51.0ms	(*.f64 x1 (+.f64 x1 -2))

simplify47.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4945	1532
1	4945	1532

prune118.0ms (3.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	102	2	104

Merged error: 4.2b

Counts

104 → 2

Compiler

Compiled 2852 to 1786 computations (37.4% saved)

localize16.0ms (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))
4.7b	(log.f64 (exp.f64 (-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)))
5.8b	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)

rewrite48.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64_2457`
35×	`*-un-lft-identity_binary64_2436`
20×	`times-frac_binary64_2442`
17×	`add-cube-cbrt_binary64_2468`
12×	`difference-of-squares_binary64_2405`
8×	`add-log-exp_binary64_2472`
7×	`log-pow_binary64_2522`
6×	`distribute-lft-out--_binary64_2390` `add-exp-log_binary64_2471` `exp-prod_binary64_2485` `associate-/r*_binary64_2382` `add-cbrt-cube_binary64_2469`
5×	`pow1_binary64_2494`
4×	`log-prod_binary64_2519`
3×	`associate-/l*_binary64_2383`
2×	`associate-/r/_binary64_2384` `flip3--_binary64_2440` `flip--_binary64_2411` `sub-neg_binary64_2429`
1×	`flip3-+_binary64_2439` `distribute-lft-out_binary64_2389` `cbrt-undiv_binary64_2467` `exp-diff_binary64_2481` `flip-+_binary64_2410` `div-inv_binary64_2433` `diff-log_binary64_2525` `div-exp_binary64_2484` `sum-log_binary64_2524` `clear-num_binary64_2435` `log-div_binary64_2520` `+-commutative_binary64_2368` `frac-2neg_binary64_2447` `rem-log-exp_binary64_2474` `exp-sum_binary64_2479`

Counts

4 → 87

Calls

4 calls:

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

series574.0ms (18.4%)

Counts

4 → 12

Calls

4 calls:

316.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)))
138.0ms	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)
61.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
58.0ms	(/.f64 x0 (-.f64 1 x1))

simplify63.0ms (2%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5006	1762

prune130.0ms (4.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	97	2	99
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	99	2	101

Merged error: 3.1b

Counts

101 → 2

Compiler

Compiled 2955 to 1909 computations (35.4% saved)

regimes20.0ms (0.6%)

Compiler: Compiled 136 to 108 computations (20.6% saved)

bsearch16.0ms (0.5%)

Steps

Iters	Range		Point
7	0.000209	0.0186	0.00021208908081054686

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	58	108
1	58	108

end0.0ms (0%)

sample685.0ms (22%)

Algorithm

1×

intervals

Results

239.0ms	8000×	pre	128	true
183.0ms	8000×	body	128	valid

Compiler

Compiled 165 to 126 computations (23.6% saved)

Details

analyze3.0ms (0.1%)

sample18.0ms (0.6%)

simplify198.0ms (6.3%)

prune2.0ms (0.1%)

localize8.0ms (0.3%)

rewrite24.0ms (0.8%)

series124.0ms (4%)

simplify62.0ms (2%)

prune46.0ms (1.5%)

localize12.0ms (0.4%)

rewrite56.0ms (1.8%)

series258.0ms (8.3%)

simplify78.0ms (2.5%)

prune149.0ms (4.8%)

localize12.0ms (0.4%)

rewrite44.0ms (1.4%)

series305.0ms (9.8%)

simplify47.0ms (1.5%)

prune118.0ms (3.8%)

localize16.0ms (0.5%)

rewrite48.0ms (1.5%)

series574.0ms (18.4%)

simplify63.0ms (2%)

prune130.0ms (4.2%)

regimes20.0ms (0.6%)

bsearch16.0ms (0.5%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample685.0ms (22%)

Profiling