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 8 to 7 computations (12.5% saved)

sample68.0ms (1.4%)

Algorithm

1×

intervals

Results

31.0ms	112×	body	1024	valid
18.0ms	39×	body	2048	valid
7.0ms	36×	body	512	valid
3.0ms	27×	body	256	valid
3.0ms	42×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify108.0ms (2.3%)

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

37.6b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.4b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.7b	(sin.f64 (+.f64 x eps))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
4×	`add-log-exp_binary64_2163`
3×	`cancel-sign-sub-inv_binary64_2090` `add-cube-cbrt_binary64_2159`
2×	`pow1_binary64_2185` `sin-sum_binary64_2257` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
1×	`flip--_binary64_2099` `difference-of-squares_binary64_2093` `flip3--_binary64_2128` `distribute-lft-out--_binary64_2076` `diff-sin_binary64_2274` `diff-log_binary64_2216` `associate--l+_binary64_2061` `sub-neg_binary64_2117`

Counts

2 → 26

Calls

2 calls:

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

series49.0ms (1%)

Counts

2 → 6

Calls

2 calls:

32.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
16.0ms	(sin.f64 (+.f64 x eps))

simplify58.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5196	441

prune31.0ms (0.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	29	3	32
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	30	3	33

Error

0.3b

Counts

33 → 3

Compiler

Compiled 428 to 129 computations (69.9% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (+.f64 x eps))
0.2b	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
4.5b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite22.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_2124`
8×	`add-log-exp_binary64_2163`
7×	`add-sqr-sqrt_binary64_2146`
5×	`pow1_binary64_2185` `add-cube-cbrt_binary64_2159` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
3×	`sum-log_binary64_2215` `distribute-lft-out_binary64_2075` `associate-l_binary64_2065` `associate-r_binary64_2064`
1×	`pow-prod-down_binary64_2195` `sin-cos-mult_binary64_2280` `unswap-sqr_binary64_2092` `*-commutative_binary64_2055` `associate-+r+_binary64_2056` `prod-exp_binary64_2173` `+-commutative_binary64_2054` `flip3-+_binary64_2127` `flip-+_binary64_2098` `cbrt-unprod_binary64_2157`

Counts

3 → 41

Calls

3 calls:

7.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
6.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
6.0ms	(+.f64 x (+.f64 x eps))

series83.0ms (1.8%)

Counts

3 → 9

Calls

3 calls:

47.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
20.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
15.0ms	(+.f64 x (+.f64 x eps))

simplify83.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5266	830

prune69.0ms (1.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	44	6	50
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	44	9	53

Error

0.3b

Counts

53 → 9

Compiler

Compiled 1211 to 789 computations (34.8% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
0.2b	(*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))))
0.4b	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
4.5b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite43.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_2146`
12×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
9×	`log-prod_binary64_2210` `exp-prod_binary64_2176`
8×	`log-pow_binary64_2213` `pow1_binary64_2185`
7×	`associate-r_binary64_2064`
6×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
5×	`add-log-exp_binary64_2163`
3×	`associate-l_binary64_2065` `distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073`
1×	`pow-prod-down_binary64_2195` `rem-log-exp_binary64_2165` `unswap-sqr_binary64_2092` `*-commutative_binary64_2055` `prod-exp_binary64_2173` `rem-exp-log_binary64_2164` `cbrt-unprod_binary64_2157`

Counts

4 → 61

Calls

4 calls:

14.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))))
9.0ms	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
8.0ms	(exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series208.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

95.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))))
60.0ms	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
35.0ms	(exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
19.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify77.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4989	1476
1	4989	1476

prune102.0ms (2.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	70	3	73
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	73	9	82

Error

0.3b

Counts

82 → 9

Compiler

Compiled 1897 to 1262 computations (33.5% saved)

localize22.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.4b	(cbrt.f64 (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))))
4.5b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
4.5b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
4.5b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite28.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`cbrt-prod_binary64_2155`
6×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
5×	`pow1_binary64_2185`
4×	`log-pow_binary64_2213` `add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
3×	`exp-prod_binary64_2176`
1×	`pow1/3_binary64_2206`

Counts

4 → 36

Calls

4 calls:

8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
7.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
7.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
2.0ms	(cbrt.f64 (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))))

series189.0ms (4%)

Counts

4 → 12

Calls

4 calls:

135.0ms	(cbrt.f64 (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))))
19.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
17.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
17.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify65.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4889	745
1	4889	745

prune88.0ms (1.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	48	0	48
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	48	9	57

Error

0.3b

Counts

57 → 9

Compiler

Compiled 1991 to 1190 computations (40.2% saved)

regimes277.0ms (5.8%)

Accuracy

Total 0.1b remaining (24.2%)

Threshold costs 0.1b (24.2%)

Compiler

Compiled 1854 to 1400 computations (24.5% saved)

bsearch69.0ms (1.5%)

Steps

Iters	Range		Point
11	1.9897327575943538e-11	3747872427711438.5	1.6499522829369943e-08
7	-0.006400558271938249	-7.576352140883233e-05	-7.728874070215344e-05

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	47	57
1	47	57

end0.0ms (0%)

sample2.9s (62.2%)

Algorithm

1×

intervals

Results

1.0s	3500×	body	1024	valid
623.0ms	1207×	body	2048	valid
259.0ms	1326×	body	512	valid
88.0ms	622×	body	256	valid
82.0ms	1342×	body	128	valid
3.0ms	3×	body	4096	valid

Compiler

Compiled 669 to 508 computations (24.1% saved)

Details

analyze2.0ms (0%)

sample68.0ms (1.4%)

simplify108.0ms (2.3%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite13.0ms (0.3%)

series49.0ms (1%)

simplify58.0ms (1.2%)

prune31.0ms (0.6%)

localize11.0ms (0.2%)

rewrite22.0ms (0.5%)

series83.0ms (1.8%)

simplify83.0ms (1.8%)

prune69.0ms (1.5%)

localize15.0ms (0.3%)

rewrite43.0ms (0.9%)

series208.0ms (4.4%)

simplify77.0ms (1.6%)

prune102.0ms (2.2%)

localize22.0ms (0.5%)

rewrite28.0ms (0.6%)

series189.0ms (4%)

simplify65.0ms (1.4%)

prune88.0ms (1.9%)

regimes277.0ms (5.8%)

bsearch69.0ms (1.5%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample2.9s (62.2%)

Profiling