Details

analyze1.2s (4%)

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)

sample114.0ms (0.4%)

Algorithm

1×

intervals

Results

48.0ms	120×	body	1024	valid
32.0ms	28×	body	2048	valid
11.0ms	44×	body	512	valid
4.0ms	45×	body	128	valid
3.0ms	18×	body	256	valid
2.0ms	1×	body	4096	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify10.0ms (0%)

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

33.8b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

1.3b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.4b	(tan.f64 (+.f64 x eps))

rewrite50.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Error

19.9b

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:

9.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
4.0ms	(tan.f64 (+.f64 x eps))

Compiler

Compiled 416 to 108 computations (74% saved)

series534.0ms (1.9%)

Error

11.7b

Counts

2 → 22

Calls

2 calls:

297.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
191.0ms	(tan.f64 (+.f64 x eps))

Compiler

Compiled 1547 to 912 computations (41% saved)

simplify46.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5115	1342

prune80.0ms (0.3%)

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%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
0.1b	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
2.2b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite162.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

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` `div-exp_binary64_2175` `cbrt-undiv_binary64_2158` `frac-2neg_binary64_2135` `clear-num_binary64_2123` `div-inv_binary64_2121` `sum-log_binary64_2215` `+-commutative_binary64_2054`

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)

series2.1s (7.5%)

Error

0.1b

Counts

4 → 40

Calls

4 calls:

1.1s	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
572.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
223.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
203.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

Compiler

Compiled 3195 to 1731 computations (45.8% saved)

simplify73.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5281	3741

prune260.0ms (0.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	120	8	128
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	122	10	132

Error

0.1b

Counts

132 → 10

Compiler

Compiled 3814 to 1339 computations (64.9% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.3b	(.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))
0.3b	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)
2.2b	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3))) (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps))) (.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))

rewrite369.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

48×	`pow1_binary64_2185`
45×	`tan-quot_binary64_2283`
21×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160` `frac-times_binary64_2134`
19×	`pow-prod-down_binary64_2195`
15×	`associate-*r/_binary64_2066`
14×	`associate-*l/_binary64_2067`
10×	`add-sqr-sqrt_binary64_2146` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
8×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
6×	`add-log-exp_binary64_2163`
5×	`frac-sub_binary64_2133`
4×	`pow-prod-up_binary64_2194` `pow-sqr_binary64_2097` `associate-l_binary64_2065` `associate-r_binary64_2064`
3×	`cancel-sign-sub-inv_binary64_2090` `pow-unpow_binary64_2201` `cube-div_binary64_2153`
2×	`flip3-+_binary64_2127` `flip-+_binary64_2098` `associate--l+_binary64_2061` `pow-pow_binary64_2196` `pow-exp_binary64_2192` `rem-cube-cbrt_binary64_2147` `pow-plus_binary64_2187` `*-commutative_binary64_2055`
1×	`diff-log_binary64_2216` `flip3--_binary64_2128` `sub-neg_binary64_2117` `flip--_binary64_2099` `distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073` `unpow-prod-down_binary64_2203` `pow-to-exp_binary64_2193` `unpow3_binary64_2190` `cube-mult_binary64_2154` `cube-prod_binary64_2152` `sqr-pow_binary64_2096` `pow2_binary64_2205` `swap-sqr_binary64_2091` `unswap-sqr_binary64_2092`

Counts

4 → 116

Calls

4 calls:

27.0ms	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3))) (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps))) (.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))
15.0ms	(.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))
11.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
5.0ms	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)

Compiler

Compiled 6413 to 2246 computations (65% saved)

series7.7s (26.8%)

Error

0.1b

Counts

4 → 34

Calls

4 calls:

6.5s	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3))) (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps))) (.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))
448.0ms	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)
377.0ms	(.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))
246.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

Compiler

Compiled 6765 to 3973 computations (41.3% saved)

simplify100.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5043	4992

prune388.0ms (1.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	146	4	150
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	150	10	160

Error

0.1b

Counts

160 → 10

Compiler

Compiled 8210 to 3253 computations (60.4% saved)

localize46.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))
0.3b	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)
2.2b	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (cbrt.f64 (pow.f64 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3) 3)))) (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps))) (.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))
8.3b	(cbrt.f64 (pow.f64 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3) 3))

rewrite398.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

46×	`pow1_binary64_2185`
45×	`tan-quot_binary64_2283`
22×	`cbrt-prod_binary64_2155`
21×	`frac-times_binary64_2134`
19×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
18×	`pow-prod-down_binary64_2195`
15×	`associate-*r/_binary64_2066`
14×	`associate-*l/_binary64_2067`
11×	`unpow-prod-down_binary64_2203` `cube-prod_binary64_2152`
9×	`add-cube-cbrt_binary64_2159` `cube-div_binary64_2153` `add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
6×	`add-log-exp_binary64_2163`
5×	`frac-sub_binary64_2133`
4×	`unpow3_binary64_2190` `cube-mult_binary64_2154` `sqr-pow_binary64_2096` `pow-prod-up_binary64_2194` `pow-sqr_binary64_2097`
3×	`cbrt-div_binary64_2156` `cancel-sign-sub-inv_binary64_2090` `pow-unpow_binary64_2201`
2×	`flip3-+_binary64_2127` `flip-+_binary64_2098` `associate--l+_binary64_2061` `pow-pow_binary64_2196` `pow-exp_binary64_2192` `rem-cube-cbrt_binary64_2147` `pow-plus_binary64_2187`
1×	`pow1/3_binary64_2206` `rem-cbrt-cube_binary64_2148` `diff-log_binary64_2216` `flip3--_binary64_2128` `sub-neg_binary64_2117` `flip--_binary64_2099` `distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073` `pow-to-exp_binary64_2193` `pow2_binary64_2205` `swap-sqr_binary64_2091` `associate-l_binary64_2065` `associate-r_binary64_2064` `*-commutative_binary64_2055`

Counts

4 → 129

Calls

4 calls:

37.0ms	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (cbrt.f64 (pow.f64 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3) 3)))) (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps))) (.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))
11.0ms	(.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))
7.0ms	(cbrt.f64 (pow.f64 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3) 3))
6.0ms	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)

Compiler

Compiled 7636 to 3028 computations (60.3% saved)

series7.7s (26.7%)

Error

0.1b

Counts

4 → 33

Calls

4 calls:

6.3s	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (cbrt.f64 (pow.f64 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3) 3)))) (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps))) (.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))
440.0ms	(cbrt.f64 (pow.f64 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3) 3))
439.0ms	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)
412.0ms	(.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))

Compiler

Compiled 6859 to 4150 computations (39.5% saved)

simplify112.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5080	5457

prune425.0ms (1.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	159	3	162
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	160	12	172

Error

0.1b

Counts

172 → 12

Compiler

Compiled 8661 to 3621 computations (58.2% saved)

regimes1.5s (5.1%)

Accuracy

Total 0.2b remaining (70%)

Threshold costs 0.2b (70%)

Compiler

Compiled 14816 to 8512 computations (42.5% saved)

bsearch95.0ms (0.3%)

Steps

Iters	Range		Point
7	3.353568808107631e-05	0.0037483165306366638	0.00023798155281232094
9	-15.520563085844756	-7.462007066676984e-07	-0.00018789018785287954

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	148	351
1	148	351

end0.0ms (0%)

sample5.3s (18.3%)

Algorithm

1×

intervals

Results

815.0ms	3555×	body	1024	valid
497.0ms	1175×	body	2048	valid
198.0ms	1381×	body	512	valid
61.0ms	1314×	body	128	valid
53.0ms	573×	body	256	valid
2.0ms	2×	body	4096	valid

Compiler

Compiled 5151 to 2947 computations (42.8% saved)

Details

analyze1.2s (4%)

sample114.0ms (0.4%)

simplify10.0ms (0%)

prune2.0ms (0%)

localize6.0ms (0%)

rewrite50.0ms (0.2%)

series534.0ms (1.9%)

simplify46.0ms (0.2%)

prune80.0ms (0.3%)

localize10.0ms (0%)

rewrite162.0ms (0.6%)

series2.1s (7.5%)

simplify73.0ms (0.3%)

prune260.0ms (0.9%)

localize25.0ms (0.1%)

rewrite369.0ms (1.3%)

series7.7s (26.8%)

simplify100.0ms (0.3%)

prune388.0ms (1.4%)

localize46.0ms (0.2%)

rewrite398.0ms (1.4%)

series7.7s (26.7%)

simplify112.0ms (0.4%)

prune425.0ms (1.5%)

regimes1.5s (5.1%)

bsearch95.0ms (0.3%)

simplify5.0ms (0%)

end0.0ms (0%)

sample5.3s (18.3%)

Profiling