Details

analyze2.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	0%	50%	4

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample39.0ms (1.2%)

Algorithm

1×

intervals

Results

18.0ms	78×	body	1024	valid
7.0ms	124×	body	128	valid
4.0ms	30×	body	512	valid
2.0ms	6×	body	2048	valid
2.0ms	18×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify177.0ms (5.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

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: 31.3b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

2.9b	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
3.7b	(log.f64 (+.f64 N 1))

rewrite14.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64_423`
11×	`log-prod_binary64_509`
8×	`add-sqr-sqrt_binary64_445` `pow1_binary64_484`
6×	`add-cube-cbrt_binary64_458` `log-pow_binary64_512`
4×	`associate--l+_binary64_360` `cancel-sign-sub-inv_binary64_389` `distribute-lft-out--_binary64_375` `log-div_binary64_510`
3×	`associate--r+_binary64_359` `add-exp-log_binary64_461`
2×	`flip-+_binary64_397` `associate--l-_binary64_361` `distribute-lft-out_binary64_374` `flip3-+_binary64_426` `add-cbrt-cube_binary64_459` `add-log-exp_binary64_462`
1×	`sub-neg_binary64_416` `diff-log_binary64_515` `flip3--_binary64_427` `rem-log-exp_binary64_464` `difference-of-squares_binary64_392` `flip--_binary64_398`

Counts

2 → 44

Calls

2 calls:

8.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
4.0ms	(log.f64 (+.f64 N 1))

series78.0ms (2.5%)

Counts

2 → 6

Calls

2 calls:

54.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
25.0ms	(log.f64 (+.f64 N 1))

simplify67.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5011	673

prune116.0ms (3.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	47	3	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	3	51

Merged error: 0.0b

Counts

51 → 3

Compiler

Compiled 1478 to 1115 computations (24.6% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3)))
0.4b	(/.f64 1/3 (pow.f64 N 3))
0.5b	(/.f64 1/2 (*.f64 N N))
9.2b	(-.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))) (/.f64 1/2 (*.f64 N N)))

rewrite93.0ms (3%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary64_423`
45×	`times-frac_binary64_429`
37×	`add-sqr-sqrt_binary64_445`
33×	`add-cube-cbrt_binary64_458`
14×	`add-exp-log_binary64_461`
13×	`associate-/r*_binary64_367`
12×	`cube-prod_binary64_451` `unpow-prod-down_binary64_502`
11×	`add-cbrt-cube_binary64_459` `add-log-exp_binary64_462`
7×	`cancel-sign-sub-inv_binary64_389`
6×	`associate-/l*_binary64_368`
5×	`distribute-lft-out_binary64_374` `div-inv_binary64_420` `div-exp_binary64_474`
4×	`unpow3_binary64_489` `pow1_binary64_484` `cube-mult_binary64_453` `sqr-pow_binary64_395`
3×	`distribute-lft-out--_binary64_375` `cbrt-undiv_binary64_457` `frac-sub_binary64_432`
2×	`frac-add_binary64_431` `flip-+_binary64_397` `diff-log_binary64_515` `clear-num_binary64_422` `flip3-+_binary64_426` `frac-2neg_binary64_434` `difference-of-squares_binary64_392` `sum-log_binary64_514`
1×	`associate--l+_binary64_360` `sub-neg_binary64_416` `pow-to-exp_binary64_492` `prod-exp_binary64_472` `+-commutative_binary64_353` `pow-exp_binary64_491` `flip3--_binary64_427` `flip--_binary64_398` `cbrt-unprod_binary64_456`

Counts

4 → 129

Calls

4 calls:

38.0ms	(-.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))) (/.f64 1/2 (*.f64 N N)))
34.0ms	(+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3)))
6.0ms	(/.f64 1/3 (pow.f64 N 3))
5.0ms	(/.f64 1/2 (*.f64 N N))

series188.0ms (6%)

Counts

4 → 12

Calls

4 calls:

80.0ms	(+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3)))
46.0ms	(/.f64 1/3 (pow.f64 N 3))
33.0ms	(/.f64 1/2 (*.f64 N N))
29.0ms	(-.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))) (/.f64 1/2 (*.f64 N N)))

simplify47.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5178	2222

prune170.0ms (5.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	140	1	141
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	140	4	144

Merged error: 0.0b

Counts

144 → 4

Compiler

Compiled 3046 to 2125 computations (30.2% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 1 N) (-.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1/2 (*.f64 N N))))
0.4b	(/.f64 1/3 (pow.f64 N 3))
0.5b	(/.f64 1/2 (*.f64 N N))
9.2b	(-.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1/2 (*.f64 N N)))

rewrite93.0ms (3%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`add-sqr-sqrt_binary64_445`
60×	`times-frac_binary64_429`
47×	`*-un-lft-identity_binary64_423`
35×	`add-cube-cbrt_binary64_458`
14×	`cancel-sign-sub-inv_binary64_389` `add-exp-log_binary64_461` `cube-prod_binary64_451` `unpow-prod-down_binary64_502`
13×	`associate-/r*_binary64_367`
11×	`add-cbrt-cube_binary64_459` `add-log-exp_binary64_462`
10×	`difference-of-squares_binary64_392`
8×	`associate-+r+_binary64_355`
6×	`div-inv_binary64_420` `associate-/l*_binary64_368` `sqr-pow_binary64_395`
5×	`cube-mult_binary64_453` `div-exp_binary64_474`
4×	`unpow3_binary64_489` `distribute-lft-out_binary64_374` `pow1_binary64_484` `distribute-lft-out--_binary64_375`
3×	`frac-add_binary64_431` `cbrt-undiv_binary64_457`
2×	`sub-neg_binary64_416` `diff-log_binary64_515` `flip3--_binary64_427` `clear-num_binary64_422` `frac-2neg_binary64_434` `flip--_binary64_398` `frac-sub_binary64_432` `sum-log_binary64_514`
1×	`pow-to-exp_binary64_492` `flip-+_binary64_397` `prod-exp_binary64_472` `+-commutative_binary64_353` `pow-exp_binary64_491` `flip3-+_binary64_426` `associate-+r-_binary64_357` `cbrt-unprod_binary64_456`

Counts

4 → 145

Calls

4 calls:

42.0ms	(+.f64 (/.f64 1 N) (-.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1/2 (*.f64 N N))))
27.0ms	(-.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1/2 (*.f64 N N)))
6.0ms	(/.f64 1/3 (pow.f64 N 3))
5.0ms	(/.f64 1/2 (*.f64 N N))

series233.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

118.0ms	(-.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1/2 (*.f64 N N)))
48.0ms	(/.f64 1/3 (pow.f64 N 3))
38.0ms	(/.f64 1/2 (*.f64 N N))
29.0ms	(+.f64 (/.f64 1 N) (-.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1/2 (*.f64 N N))))

simplify53.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4959	2680
1	4959	2680

prune183.0ms (5.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	157	0	157
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	157	4	161

Merged error: 0.0b

Counts

161 → 4

Compiler

Compiled 3315 to 2293 computations (30.8% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (+.f64 N 1) N)
2.8b	(log.f64 (/.f64 (+.f64 N 1) N))

rewrite16.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64_423`
24×	`times-frac_binary64_429`
19×	`add-cube-cbrt_binary64_458` `add-sqr-sqrt_binary64_445`
16×	`log-prod_binary64_509`
7×	`distribute-lft-out_binary64_374` `add-exp-log_binary64_461`
4×	`add-cbrt-cube_binary64_459` `associate-/l*_binary64_368`
3×	`pow1_binary64_484` `associate-/r*_binary64_367`
2×	`associate-/l/_binary64_370` `rem-log-exp_binary64_464` `add-log-exp_binary64_462` `div-inv_binary64_420` `div-exp_binary64_474`
1×	`flip-+_binary64_397` `log-pow_binary64_512` `clear-num_binary64_422` `flip3-+_binary64_426` `frac-2neg_binary64_434` `log-div_binary64_510` `cbrt-undiv_binary64_457`

Counts

2 → 60

Calls

2 calls:

6.0ms	(/.f64 (+.f64 N 1) N)
5.0ms	(log.f64 (/.f64 (+.f64 N 1) N))

series120.0ms (3.8%)

Counts

2 → 6

Calls

2 calls:

76.0ms	(/.f64 (+.f64 N 1) N)
43.0ms	(log.f64 (/.f64 (+.f64 N 1) N))

simplify72.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5428	940

prune58.0ms (1.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	1	0	1
Picked	1	0	1
Done	0	2	2
Total	67	3	70

Merged error: 0.0b

Counts

70 → 3

Compiler

Compiled 909 to 626 computations (31.1% saved)

regimes15.0ms (0.5%)

Compiler: Compiled 44 to 35 computations (20.5% saved)

bsearch19.0ms (0.6%)

Steps

Iters	Range		Point
8	674.7915342854312	1054660.8908660875	4995.222351357758

Compiler

Compiled 1 to 1 computations (0% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	50	46
1	50	46

end0.0ms (0%)

sample1.3s (39.9%)

Algorithm

1×

intervals

Results

497.0ms	2082×	body	1024	valid
244.0ms	4184×	body	128	valid
146.0ms	991×	body	512	valid
94.0ms	241×	body	2048	valid
48.0ms	502×	body	256	valid

Compiler

Compiled 80 to 63 computations (21.3% saved)

Details

analyze2.0ms (0.1%)

sample39.0ms (1.2%)

simplify177.0ms (5.6%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

rewrite14.0ms (0.5%)

series78.0ms (2.5%)

simplify67.0ms (2.1%)

prune116.0ms (3.7%)

localize10.0ms (0.3%)

rewrite93.0ms (3%)

series188.0ms (6%)

simplify47.0ms (1.5%)

prune170.0ms (5.4%)

localize10.0ms (0.3%)

rewrite93.0ms (3%)

series233.0ms (7.4%)

simplify53.0ms (1.7%)

prune183.0ms (5.8%)

localize5.0ms (0.2%)

rewrite16.0ms (0.5%)

series120.0ms (3.8%)

simplify72.0ms (2.3%)

prune58.0ms (1.9%)

regimes15.0ms (0.5%)

bsearch19.0ms (0.6%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.3s (39.9%)

Profiling