Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 11 to 12 computations (-9.1% saved)

sample33.0ms (0.6%)

Algorithm

1×

intervals

Results

15.0ms	66×	body	1024	valid
5.0ms	146×	body	128	valid
4.0ms	31×	body	512	valid
1.0ms	10×	body	256	valid
1.0ms	3×	body	2048	valid

Compiler

Compiled 21 to 25 computations (-19% saved)

simplify247.0ms (4.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4638	15
1	4638	15

prune2.0ms (0%)

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: 27.4b

Counts

2 → 1

Compiler

Compiled 20 to 22 computations (-10% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 1 (exp.f64 (*.f64 -2 x)))
0.0b	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
2.0b	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)

rewrite29.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`*-un-lft-identity_binary64_423`
24×	`add-sqr-sqrt_binary64_445`
15×	`times-frac_binary64_429`
13×	`add-cube-cbrt_binary64_458`
7×	`add-log-exp_binary64_462`
5×	`distribute-lft-out_binary64_374` `add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
4×	`difference-of-squares_binary64_392` `associate-/r*_binary64_367`
3×	`cancel-sign-sub-inv_binary64_389` `pow1_binary64_484` `associate-/l*_binary64_368`
2×	`flip-+_binary64_397` `associate-/r/_binary64_369` `flip3-+_binary64_426` `difference-of-sqr-1_binary64_393`
1×	`sub-neg_binary64_416` `diff-log_binary64_515` `+-commutative_binary64_353` `flip3--_binary64_427` `clear-num_binary64_422` `distribute-lft-out--_binary64_375` `frac-2neg_binary64_434` `flip--_binary64_398` `div-inv_binary64_420` `cbrt-undiv_binary64_457` `div-exp_binary64_474` `sum-log_binary64_514`

Counts

3 → 66

Calls

3 calls:

14.0ms	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)
6.0ms	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
4.0ms	(+.f64 1 (exp.f64 (*.f64 -2 x)))

series151.0ms (2.9%)

Counts

3 → 9

Calls

3 calls:

86.0ms	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)
52.0ms	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
12.0ms	(+.f64 1 (exp.f64 (*.f64 -2 x)))

simplify107.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	4817	1373
1	4817	1373

prune231.0ms (4.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	71	4	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	4	76

Merged error: 0.0b

Counts

76 → 4

Compiler

Compiled 3451 to 3328 computations (3.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (+.f64 1 (exp.f64 (.f64 -2 x))) (+.f64 1 (exp.f64 (*.f64 -2 x))))
0.0b	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
0.0b	(/.f64 4 (.f64 (+.f64 1 (exp.f64 (.f64 -2 x))) (+.f64 1 (exp.f64 (*.f64 -2 x)))))
1.9b	(+.f64 (/.f64 4 (.f64 (+.f64 1 (exp.f64 (.f64 -2 x))) (+.f64 1 (exp.f64 (*.f64 -2 x))))) -1)

rewrite60.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64_423`
23×	`add-sqr-sqrt_binary64_445`
19×	`add-cube-cbrt_binary64_458`
16×	`times-frac_binary64_429`
14×	`flip-+_binary64_397` `flip3-+_binary64_426`
13×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
11×	`distribute-lft-out_binary64_374` `pow1_binary64_484`
10×	`associate-/r/_binary64_369`
8×	`frac-times_binary64_433`
6×	`swap-sqr_binary64_390` `add-log-exp_binary64_462` `associate-/l*_binary64_368`
5×	`associate-/r*_binary64_367`
4×	`associate-l_binary64_364` `associate-r/_binary64_365` `associate-l/_binary64_366` `associate-r_binary64_363`
3×	`cbrt-undiv_binary64_457` `div-exp_binary64_474`
2×	`prod-exp_binary64_472` `clear-num_binary64_422` `frac-2neg_binary64_434` `div-inv_binary64_420` `difference-of-sqr--1_binary64_394` `cbrt-unprod_binary64_456`
1×	`pow-prod-down_binary64_494` `distribute-rgt-in_binary64_373` `distribute-lft-in_binary64_372` `pow-sqr_binary64_396` `+-commutative_binary64_353` `pow-prod-up_binary64_493` `*-commutative_binary64_354` `pow-plus_binary64_486` `unswap-sqr_binary64_391` `pow2_binary64_504` `sum-log_binary64_514`

Counts

4 → 116

Calls

4 calls:

16.0ms	(+.f64 (/.f64 4 (.f64 (+.f64 1 (exp.f64 (.f64 -2 x))) (+.f64 1 (exp.f64 (*.f64 -2 x))))) -1)
11.0ms	(/.f64 4 (.f64 (+.f64 1 (exp.f64 (.f64 -2 x))) (+.f64 1 (exp.f64 (*.f64 -2 x)))))
11.0ms	(.f64 (+.f64 1 (exp.f64 (.f64 -2 x))) (+.f64 1 (exp.f64 (*.f64 -2 x))))
8.0ms	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))

series323.0ms (6.3%)

Counts

4 → 12

Calls

4 calls:

130.0ms	(+.f64 (/.f64 4 (.f64 (+.f64 1 (exp.f64 (.f64 -2 x))) (+.f64 1 (exp.f64 (*.f64 -2 x))))) -1)
107.0ms	(/.f64 4 (.f64 (+.f64 1 (exp.f64 (.f64 -2 x))) (+.f64 1 (exp.f64 (*.f64 -2 x)))))
53.0ms	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
33.0ms	(.f64 (+.f64 1 (exp.f64 (.f64 -2 x))) (+.f64 1 (exp.f64 (*.f64 -2 x))))

simplify75.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5026	2390

prune285.0ms (5.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	129	3	132

Merged error: 0.0b

Counts

132 → 3

Compiler

Compiled 4448 to 4002 computations (10% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
0.0b	(/.f64 4 (pow.f64 (+.f64 1 (exp.f64 (*.f64 -2 x))) 2))
1.9b	(log.f64 (exp.f64 (+.f64 (/.f64 4 (pow.f64 (+.f64 1 (exp.f64 (*.f64 -2 x))) 2)) -1)))
1.9b	(+.f64 (/.f64 4 (pow.f64 (+.f64 1 (exp.f64 (*.f64 -2 x))) 2)) -1)

rewrite66.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`*-un-lft-identity_binary64_423`
47×	`times-frac_binary64_429` `add-sqr-sqrt_binary64_445`
33×	`add-cube-cbrt_binary64_458`
18×	`unpow-prod-down_binary64_502`
13×	`associate-/r*_binary64_367`
11×	`add-exp-log_binary64_461`
10×	`distribute-lft-out_binary64_374` `log-pow_binary64_512` `difference-of-sqr--1_binary64_394`
9×	`exp-prod_binary64_475`
8×	`add-cbrt-cube_binary64_459`
6×	`add-log-exp_binary64_462` `unpow2_binary64_488` `associate-/l*_binary64_368` `sqr-pow_binary64_395`
5×	`pow1_binary64_484`
4×	`log-prod_binary64_509` `div-exp_binary64_474`
2×	`flip-+_binary64_397` `associate-/r/_binary64_369` `clear-num_binary64_422` `flip3-+_binary64_426` `frac-2neg_binary64_434` `div-inv_binary64_420` `cbrt-undiv_binary64_457`
1×	`pow-to-exp_binary64_492` `exp-sum_binary64_469` `+-commutative_binary64_353` `pow-exp_binary64_491` `rem-log-exp_binary64_464` `sum-log_binary64_514`

Counts

4 → 125

Calls

4 calls:

20.0ms	(log.f64 (exp.f64 (+.f64 (/.f64 4 (pow.f64 (+.f64 1 (exp.f64 (*.f64 -2 x))) 2)) -1)))
18.0ms	(+.f64 (/.f64 4 (pow.f64 (+.f64 1 (exp.f64 (*.f64 -2 x))) 2)) -1)
8.0ms	(/.f64 4 (pow.f64 (+.f64 1 (exp.f64 (*.f64 -2 x))) 2))
6.0ms	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))

series675.0ms (13.1%)

Counts

4 → 12

Calls

4 calls:

396.0ms	(log.f64 (exp.f64 (+.f64 (/.f64 4 (pow.f64 (+.f64 1 (exp.f64 (*.f64 -2 x))) 2)) -1)))
139.0ms	(+.f64 (/.f64 4 (pow.f64 (+.f64 1 (exp.f64 (*.f64 -2 x))) 2)) -1)
90.0ms	(/.f64 4 (pow.f64 (+.f64 1 (exp.f64 (*.f64 -2 x))) 2))
49.0ms	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))

simplify70.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4900	2839
1	4900	2839

prune317.0ms (6.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	135	2	137
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	137	3	140

Merged error: 0.0b

Counts

140 → 3

Compiler

Compiled 4851 to 4492 computations (7.4% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
0.0b	(/.f64 4 (pow.f64 (+.f64 1 (exp.f64 (*.f64 -2 x))) 2))
1.9b	(log.f64 (exp.f64 (+.f64 (/.f64 4 (pow.f64 (+.f64 1 (exp.f64 (*.f64 -2 x))) 2)) -1)))
1.9b	(+.f64 (/.f64 4 (pow.f64 (+.f64 1 (exp.f64 (*.f64 -2 x))) 2)) -1)

rewrite70.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`*-un-lft-identity_binary64_423`
47×	`times-frac_binary64_429` `add-sqr-sqrt_binary64_445`
33×	`add-cube-cbrt_binary64_458`
18×	`unpow-prod-down_binary64_502`
13×	`associate-/r*_binary64_367`
11×	`add-exp-log_binary64_461`
10×	`distribute-lft-out_binary64_374` `log-pow_binary64_512` `difference-of-sqr--1_binary64_394`
9×	`exp-prod_binary64_475`
8×	`add-cbrt-cube_binary64_459`
6×	`add-log-exp_binary64_462` `unpow2_binary64_488` `associate-/l*_binary64_368` `sqr-pow_binary64_395`
5×	`pow1_binary64_484`
4×	`log-prod_binary64_509` `div-exp_binary64_474`
2×	`flip-+_binary64_397` `associate-/r/_binary64_369` `clear-num_binary64_422` `flip3-+_binary64_426` `frac-2neg_binary64_434` `div-inv_binary64_420` `cbrt-undiv_binary64_457`
1×	`pow-to-exp_binary64_492` `exp-sum_binary64_469` `+-commutative_binary64_353` `pow-exp_binary64_491` `rem-log-exp_binary64_464` `sum-log_binary64_514`

Counts

4 → 125

Calls

4 calls:

20.0ms	(log.f64 (exp.f64 (+.f64 (/.f64 4 (pow.f64 (+.f64 1 (exp.f64 (*.f64 -2 x))) 2)) -1)))
18.0ms	(+.f64 (/.f64 4 (pow.f64 (+.f64 1 (exp.f64 (*.f64 -2 x))) 2)) -1)
11.0ms	(/.f64 4 (pow.f64 (+.f64 1 (exp.f64 (*.f64 -2 x))) 2))
6.0ms	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))

series669.0ms (12.9%)

Counts

4 → 12

Calls

4 calls:

390.0ms	(log.f64 (exp.f64 (+.f64 (/.f64 4 (pow.f64 (+.f64 1 (exp.f64 (*.f64 -2 x))) 2)) -1)))
131.0ms	(+.f64 (/.f64 4 (pow.f64 (+.f64 1 (exp.f64 (*.f64 -2 x))) 2)) -1)
95.0ms	(/.f64 4 (pow.f64 (+.f64 1 (exp.f64 (*.f64 -2 x))) 2))
52.0ms	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))

simplify70.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4900	2839
1	4900	2839

prune321.0ms (6.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	137	3	140

Merged error: 0.0b

Counts

140 → 3

Compiler

Compiled 4622 to 4273 computations (7.6% saved)

regimes172.0ms (3.3%)

Compiler: Compiled 593 to 604 computations (-1.9% saved)

bsearch1.0ms (0%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	72	82
1	72	82

end0.0ms (0%)

sample1.1s (21.9%)

Algorithm

1×

intervals

Results

422.0ms	1910×	body	1024	valid
161.0ms	4402×	body	128	valid
125.0ms	965×	body	512	valid
54.0ms	207×	body	2048	valid
46.0ms	516×	body	256	valid

Compiler

Compiled 136 to 133 computations (2.2% saved)

Details

analyze2.0ms (0%)

sample33.0ms (0.6%)

simplify247.0ms (4.8%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite29.0ms (0.6%)

series151.0ms (2.9%)

simplify107.0ms (2.1%)

prune231.0ms (4.5%)

localize12.0ms (0.2%)

rewrite60.0ms (1.2%)

series323.0ms (6.3%)

simplify75.0ms (1.4%)

prune285.0ms (5.5%)

localize18.0ms (0.3%)

rewrite66.0ms (1.3%)

series675.0ms (13.1%)

simplify70.0ms (1.4%)

prune317.0ms (6.1%)

localize18.0ms (0.3%)

rewrite70.0ms (1.4%)

series669.0ms (12.9%)

simplify70.0ms (1.4%)

prune321.0ms (6.2%)

regimes172.0ms (3.3%)

bsearch1.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.1s (21.9%)

Profiling