Details

analyze883.0ms (6.5%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	117	22
1	117	22
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.2%	0.1%	6
21.9%	78%	0.1%	7
23.4%	76.5%	0.1%	8
24.2%	75.7%	0.1%	9
24.6%	75.3%	0.1%	10
24.8%	75.1%	0.1%	11
24.9%	75%	0.1%	12
24.9%	75%	0.1%	13
25%	75%	0.1%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample71.0ms (0.5%)

Algorithm

1×

intervals

Results

26.0ms	108×	body	1024	valid
24.0ms	45×	body	2048	valid
6.0ms	44×	body	512	valid
2.0ms	20×	body	256	valid
2.0ms	39×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	72	11
1	72	11

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

Error

33.5b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

1.2b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
2.6b	(tan.f64 (+.f64 x eps))

rewrite40.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

20.9b

Rules

5×	`add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
4×	`tan-quot_binary64_2283` `add-log-exp_binary64_2163`
3×	`add-cube-cbrt_binary64_2159` `cancel-sign-sub-inv_binary64_2090`
2×	`tan-sum_binary64_2259` `pow1_binary64_2185` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160` `frac-sub_binary64_2133`
1×	`diff-log_binary64_2216` `flip3--_binary64_2128` `sub-neg_binary64_2117` `flip--_binary64_2099` `difference-of-squares_binary64_2093` `distribute-lft-out--_binary64_2076`

Counts

2 → 27

Calls

2 calls:

7.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
4.0ms	(tan.f64 (+.f64 x eps))

Compiler

Compiled 416 to 108 computations (74% saved)

series466.0ms (3.5%)

Error

10.7b

Counts

2 → 22

Calls

2 calls:

263.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
162.0ms	(tan.f64 (+.f64 x eps))

Compiler

Compiled 1547 to 912 computations (41% saved)

simplify34.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5115	1342

prune67.0ms (0.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	45	4	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	4	50

Error

0.2b

Counts

50 → 4

Compiler

Compiled 1145 to 449 computations (60.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
1.8b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite137.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

28×	`*-un-lft-identity_binary64_2124`
23×	`add-sqr-sqrt_binary64_2146`
16×	`add-cube-cbrt_binary64_2159`
13×	`times-frac_binary64_2130`
9×	`tan-quot_binary64_2283`
8×	`add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
6×	`pow1_binary64_2185`
5×	`distribute-lft-out_binary64_2075`
4×	`associate-/l*_binary64_2069`
3×	`cancel-sign-sub-inv_binary64_2090` `associate-l_binary64_2065` `associate-r_binary64_2064` `associate-/l/_binary64_2071` `associate-/r*_binary64_2068`
2×	`flip3--_binary64_2128` `flip--_binary64_2099` `difference-of-squares_binary64_2093` `frac-add_binary64_2132` `flip3-+_binary64_2127` `flip-+_binary64_2098` `associate-/r/_binary64_2070`
1×	`diff-log_binary64_2216` `frac-sub_binary64_2133` `sub-neg_binary64_2117` `distribute-lft-out--_binary64_2076` `pow-prod-down_binary64_2195` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157` `frac-times_binary64_2134` `unswap-sqr_binary64_2092` `associate-l/_binary64_2067` `associate-r/_binary64_2066` `*-commutative_binary64_2055` `sum-log_binary64_2215` `+-commutative_binary64_2054` `div-exp_binary64_2175` `cbrt-undiv_binary64_2158` `frac-2neg_binary64_2135` `clear-num_binary64_2123` `div-inv_binary64_2121`

Counts

4 → 88

Calls

4 calls:

13.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
9.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
4.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

Compiler

Compiled 2365 to 732 computations (69% saved)

series1.8s (13.3%)

Error

0.2b

Counts

4 → 40

Calls

4 calls:

878.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
483.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
213.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
181.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

Compiler

Compiled 3195 to 1731 computations (45.8% saved)

simplify63.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5281	3741

prune160.0ms (1.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	118	10	128
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	121	11	132

Error

0.1b

Counts

132 → 11

Compiler

Compiled 3848 to 1356 computations (64.8% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 eps) (sin.f64 x))
0.3b	(/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))
0.3b	(/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))
1.8b	(-.f64 (+.f64 (/.f64 (sin.f64 x) (.f64 (cos.f64 x) (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))))) (/.f64 (sin.f64 eps) (.f64 (cos.f64 eps) (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x))))))) (/.f64 (sin.f64 x) (cos.f64 x)))

rewrite234.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

30×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
20×	`add-sqr-sqrt_binary64_2146`
18×	`*-un-lft-identity_binary64_2124`
13×	`add-cube-cbrt_binary64_2159` `cancel-sign-sub-inv_binary64_2090`
12×	`times-frac_binary64_2130`
9×	`add-log-exp_binary64_2163` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
8×	`div-exp_binary64_2175` `cbrt-undiv_binary64_2158`
6×	`pow1_binary64_2185`
3×	`frac-sub_binary64_2133` `div-inv_binary64_2121` `sin-mult_binary64_2279` `associate-l_binary64_2065` `associate-r_binary64_2064`
2×	`diff-log_binary64_2216` `difference-of-squares_binary64_2093` `distribute-lft-out--_binary64_2076` `frac-2neg_binary64_2135` `clear-num_binary64_2123` `associate-/l/_binary64_2071` `cos-mult_binary64_2278` `associate-/r/_binary64_2070` `associate-/l_binary64_2069` `associate-/r_binary64_2068`
1×	`sum-log_binary64_2215` `frac-add_binary64_2132` `flip3-+_binary64_2127` `flip-+_binary64_2098` `flip3--_binary64_2128` `sub-neg_binary64_2117` `flip--_binary64_2099` `distribute-lft-out_binary64_2075` `associate--l+_binary64_2061` `pow-prod-down_binary64_2195` `unswap-sqr_binary64_2092` `*-commutative_binary64_2055`

Counts

4 → 98

Calls

4 calls:

28.0ms	(-.f64 (+.f64 (/.f64 (sin.f64 x) (.f64 (cos.f64 x) (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))))) (/.f64 (sin.f64 eps) (.f64 (cos.f64 eps) (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x))))))) (/.f64 (sin.f64 x) (cos.f64 x)))
8.0ms	(/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))
8.0ms	(/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))
5.0ms	(*.f64 (sin.f64 eps) (sin.f64 x))

Compiler

Compiled 6105 to 1482 computations (75.7% saved)

series1.5s (11.2%)

Error

0.1b

Counts

4 → 35

Calls

4 calls:

932.0ms	(-.f64 (+.f64 (/.f64 (sin.f64 x) (.f64 (cos.f64 x) (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))))) (/.f64 (sin.f64 eps) (.f64 (cos.f64 eps) (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x))))))) (/.f64 (sin.f64 x) (cos.f64 x)))
220.0ms	(/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))
215.0ms	(/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))
95.0ms	(*.f64 (sin.f64 eps) (sin.f64 x))

Compiler

Compiled 4423 to 2024 computations (54.2% saved)

simplify93.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5046	5144

prune230.0ms (1.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	130	3	133
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	133	11	144

Error

0.1b

Counts

144 → 11

Compiler

Compiled 7836 to 2202 computations (71.9% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (sin.f64 x))
0.2b	(*.f64 (sin.f64 eps) (sin.f64 x))
0.3b	(/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))
1.8b	(-.f64 (+.f64 (/.f64 (sin.f64 x) (.f64 (cos.f64 x) (-.f64 1 (/.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (sin.f64 x)) (cos.f64 x))))) (/.f64 (sin.f64 eps) (.f64 (cos.f64 eps) (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x))))))) (/.f64 (sin.f64 x) (cos.f64 x)))

rewrite248.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

33×	`add-sqr-sqrt_binary64_2146`
26×	`*-un-lft-identity_binary64_2124`
23×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
21×	`add-cube-cbrt_binary64_2159` `times-frac_binary64_2130`
16×	`associate-l_binary64_2065`
13×	`cancel-sign-sub-inv_binary64_2090`
9×	`add-log-exp_binary64_2163`
8×	`pow1_binary64_2185`
7×	`prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
6×	`associate-r_binary64_2064`
5×	`div-exp_binary64_2175` `cbrt-undiv_binary64_2158`
3×	`frac-sub_binary64_2133` `div-inv_binary64_2121` `unswap-sqr_binary64_2092`
2×	`diff-log_binary64_2216` `difference-of-squares_binary64_2093` `distribute-lft-out--_binary64_2076` `sin-mult_binary64_2279` `pow-prod-down_binary64_2195` `*-commutative_binary64_2055`
1×	`sum-log_binary64_2215` `frac-add_binary64_2132` `flip3-+_binary64_2127` `flip-+_binary64_2098` `flip3--_binary64_2128` `sub-neg_binary64_2117` `flip--_binary64_2099` `distribute-lft-out_binary64_2075` `associate--l+_binary64_2061` `frac-2neg_binary64_2135` `clear-num_binary64_2123` `associate-/l/_binary64_2071` `cos-mult_binary64_2278` `associate-/r/_binary64_2070` `associate-/l_binary64_2069` `associate-/r_binary64_2068` `associate-*l/_binary64_2067`

Counts

4 → 107

Calls

4 calls:

27.0ms	(-.f64 (+.f64 (/.f64 (sin.f64 x) (.f64 (cos.f64 x) (-.f64 1 (/.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (sin.f64 x)) (cos.f64 x))))) (/.f64 (sin.f64 eps) (.f64 (cos.f64 eps) (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x))))))) (/.f64 (sin.f64 x) (cos.f64 x)))
8.0ms	(/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))
8.0ms	(*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (sin.f64 x))
5.0ms	(*.f64 (sin.f64 eps) (sin.f64 x))

Compiler

Compiled 6575 to 1689 computations (74.3% saved)

series1.4s (10.6%)

Error

0.1b

Counts

4 → 36

Calls

4 calls:

917.0ms	(-.f64 (+.f64 (/.f64 (sin.f64 x) (.f64 (cos.f64 x) (-.f64 1 (/.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (sin.f64 x)) (cos.f64 x))))) (/.f64 (sin.f64 eps) (.f64 (cos.f64 eps) (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x))))))) (/.f64 (sin.f64 x) (cos.f64 x)))
212.0ms	(/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))
164.0ms	(*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (sin.f64 x))
93.0ms	(*.f64 (sin.f64 eps) (sin.f64 x))

Compiler

Compiled 4529 to 2101 computations (53.6% saved)

simplify110.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4976	5195
1	4976	5195

prune222.0ms (1.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	143	11	154

Error

0.1b

Counts

154 → 11

Compiler

Compiled 7803 to 2093 computations (73.2% saved)

regimes1.0s (7.7%)

Accuracy

Total 0.5b remaining (84.2%)

Threshold costs 0.5b (84.2%)

Compiler

Compiled 11621 to 5897 computations (49.3% saved)

bsearch89.0ms (0.7%)

Steps

Iters	Range		Point
11	4.2697167763427716e-45	8.878838085910307e-20	8.767513643243207e-20
7	-0.00390156783666061	-2.0796517058321007e-05	-4.110958230728241e-05

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	105	170
1	105	170

end0.0ms (0%)

sample4.5s (33.2%)

Algorithm

1×

intervals

Results

850.0ms	3564×	body	1024	valid
508.0ms	1178×	body	2048	valid
217.0ms	1386×	body	512	valid
63.0ms	1263×	body	128	valid
62.0ms	608×	body	256	valid
1.0ms	1×	body	4096	valid

Compiler

Compiled 3977 to 2031 computations (48.9% saved)

Details

analyze883.0ms (6.5%)

sample71.0ms (0.5%)

simplify10.0ms (0.1%)

prune2.0ms (0%)

localize7.0ms (0%)

rewrite40.0ms (0.3%)

series466.0ms (3.5%)

simplify34.0ms (0.3%)

prune67.0ms (0.5%)

localize10.0ms (0.1%)

rewrite137.0ms (1%)

series1.8s (13.3%)

simplify63.0ms (0.5%)

prune160.0ms (1.2%)

localize23.0ms (0.2%)

rewrite234.0ms (1.7%)

series1.5s (11.2%)

simplify93.0ms (0.7%)

prune230.0ms (1.7%)

localize25.0ms (0.2%)

rewrite248.0ms (1.8%)

series1.4s (10.6%)

simplify110.0ms (0.8%)

prune222.0ms (1.6%)

regimes1.0s (7.7%)

bsearch89.0ms (0.7%)

simplify4.0ms (0%)

end0.0ms (0%)

sample4.5s (33.2%)

Profiling