Details

analyze270.0ms (3.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 30 to 24 computations (20% saved)

sample34.0ms (0.4%)

Algorithm

1×

intervals

Results

12.0ms	243×	body	128	valid
9.0ms	287×	pre	128	true
1.0ms	31×	body	128	nan
1.0ms	13×	body	256	valid

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify409.0ms (5.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (312.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 29.6b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.2b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
29.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite35.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_2146`
14×	`*-un-lft-identity_binary64_2124`
9×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
8×	`add-log-exp_binary64_2163` `add-cube-cbrt_binary64_2159`
6×	`difference-of-squares_binary64_2093` `associate-/l*_binary64_2069` `sqrt-prod_binary64_2140` `times-frac_binary64_2130`
5×	`pow1_binary64_2185`
4×	`flip--_binary64_2099` `flip3--_binary64_2128` `cancel-sign-sub-inv_binary64_2090`
3×	`distribute-lft-out--_binary64_2076`
2×	`cbrt-undiv_binary64_2158` `sqrt-div_binary64_2141` `diff-log_binary64_2216` `sub-neg_binary64_2117` `associate-/l/_binary64_2071` `div-exp_binary64_2175`
1×	`clear-num_binary64_2123` `sqrt-pow1_binary64_2142` `associate-/r*_binary64_2068` `rem-sqrt-square_binary64_2137` `prod-exp_binary64_2173` `pow1/2_binary64_2204` `div-sub_binary64_2129` `div-inv_binary64_2121` `cbrt-unprod_binary64_2157` `frac-2neg_binary64_2135`

Counts

4 → 74

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series286.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

117.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
68.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
66.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
34.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify90.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4899	1979
1	4899	1979

prune110.0ms (1.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	79	7	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	7	87

Merged error: 0.4b

Counts

87 → 7

Compiler

Compiled 2144 to 1283 computations (40.2% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
0.2b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.3b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

rewrite49.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
22×	`times-frac_binary64_2130`
20×	`*-un-lft-identity_binary64_2124`
17×	`cbrt-undiv_binary64_2158` `div-exp_binary64_2175`
13×	`prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
11×	`associate-/l*_binary64_2069`
10×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146`
8×	`add-log-exp_binary64_2163`
6×	`associate-/r/_binary64_2070`
5×	`distribute-lft-out_binary64_2075` `associate-/r*_binary64_2068`
4×	`pow1_binary64_2185` `flip3-+_binary64_2127` `flip-+_binary64_2098` `div-inv_binary64_2121`
2×	`clear-num_binary64_2123` `frac-2neg_binary64_2135`
1×	`flip--_binary64_2099` `flip3--_binary64_2128` `cancel-sign-sub-inv_binary64_2090` `sum-log_binary64_2215` `diff-log_binary64_2216` `+-commutative_binary64_2054` `sub-neg_binary64_2117` `associate-/l/_binary64_2071`

Counts

4 → 99

Calls

4 calls:

15.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
12.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series472.0ms (6.1%)

Counts

4 → 12

Calls

4 calls:

205.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
164.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
65.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
37.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify61.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4982	3037
1	4982	3037

prune174.0ms (2.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	101	10	111
Fresh	6	0	6
Picked	1	0	1
Done	0	0	0
Total	108	10	118

Merged error: 0.0b

Counts

118 → 10

Compiler

Compiled 3345 to 2073 computations (38% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))
0.2b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
0.3b	(/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))
0.3b	(/.f64 1 (/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))))

rewrite87.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

323×	`times-frac_binary64_2130`
165×	`*-un-lft-identity_binary64_2124`
129×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146`
52×	`add-exp-log_binary64_2162`
49×	`associate-/r*_binary64_2068`
40×	`associate-/r/_binary64_2070`
32×	`add-cbrt-cube_binary64_2160`
30×	`div-exp_binary64_2175`
23×	`div-inv_binary64_2121`
18×	`distribute-lft-out_binary64_2075`
17×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
16×	`cbrt-undiv_binary64_2158`
7×	`associate-/l*_binary64_2069`
6×	`add-log-exp_binary64_2163`
5×	`pow1_binary64_2185` `prod-exp_binary64_2173`
4×	`1-exp_binary64_2168` `rec-exp_binary64_2174`
3×	`clear-num_binary64_2123` `cbrt-unprod_binary64_2157` `frac-2neg_binary64_2135`
1×	`flip--_binary64_2099` `flip3--_binary64_2128` `cancel-sign-sub-inv_binary64_2090` `diff-log_binary64_2216` `sub-neg_binary64_2117` `pow-flip_binary64_2198` `inv-pow_binary64_2209`

Counts

4 → 269

Calls

4 calls:

19.0ms	(/.f64 1 (/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))))
13.0ms	(/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))
10.0ms	(/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))
4.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

series541.0ms (7%)

Counts

4 → 12

Calls

4 calls:

199.0ms	(/.f64 1 (/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))))
199.0ms	(/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))
109.0ms	(/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))
35.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify126.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

281 → 281

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5098	10866

prune560.0ms (7.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	278	3	281
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	282	9	291

Merged error: 0b

Counts

291 → 9

Compiler

Compiled 9173 to 6078 computations (33.7% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))) 3))))))
0.3b	(/.f64 1 (/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))) 3)))))))
0.5b	(cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3))
0.7b	(pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3)

rewrite97.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

319×	`times-frac_binary64_2130`
165×	`*-un-lft-identity_binary64_2124`
133×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146`
48×	`add-exp-log_binary64_2162`
45×	`associate-/r*_binary64_2068`
38×	`associate-/r/_binary64_2070`
28×	`add-cbrt-cube_binary64_2160` `div-exp_binary64_2175`
22×	`div-inv_binary64_2121`
16×	`distribute-lft-out_binary64_2075` `flip3-+_binary64_2127` `flip-+_binary64_2098`
14×	`cbrt-undiv_binary64_2158`
12×	`cbrt-prod_binary64_2155`
6×	`unpow-prod-down_binary64_2203` `associate-/l*_binary64_2069` `pow1_binary64_2185` `cube-prod_binary64_2152`
4×	`add-log-exp_binary64_2163` `prod-exp_binary64_2173` `cube-div_binary64_2153` `1-exp_binary64_2168` `rec-exp_binary64_2174`
3×	`pow-unpow_binary64_2201`
2×	`flip--_binary64_2099` `unpow3_binary64_2190` `cbrt-div_binary64_2156` `clear-num_binary64_2123` `flip3--_binary64_2128` `cube-mult_binary64_2154` `sqr-pow_binary64_2096` `cbrt-unprod_binary64_2157` `frac-2neg_binary64_2135`
1×	`pow-pow_binary64_2196` `rem-cbrt-cube_binary64_2148` `pow-exp_binary64_2192` `pow1/3_binary64_2206` `pow-flip_binary64_2198` `pow-to-exp_binary64_2193` `inv-pow_binary64_2209` `rem-cube-cbrt_binary64_2147`

Counts

4 → 280

Calls

4 calls:

23.0ms	(/.f64 1 (/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))) 3)))))))
16.0ms	(/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))) 3))))))
6.0ms	(pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3)
5.0ms	(cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3))

series426.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

196.0ms	(/.f64 1 (/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))) 3)))))))
115.0ms	(/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))) 3))))))
80.0ms	(pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3)
35.0ms	(cbrt.f64 (pow.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))) 3))

simplify135.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4975	11064
1	4975	11064

prune555.0ms (7.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	292	0	292
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	292	9	301

Merged error: 0b

Counts

301 → 9

Compiler

Compiled 9595 to 6399 computations (33.3% saved)

regimes755.0ms (9.7%)

Compiler: Compiled 7468 to 5698 computations (23.7% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	29
1	63	29

end0.0ms (0%)

sample2.4s (31.2%)

Algorithm

1×

intervals

Results

399.0ms	7684×	body	128	valid
278.0ms	8846×	pre	128	true
40.0ms	846×	body	128	nan
31.0ms	316×	body	256	valid

Compiler

Compiled 1906 to 1456 computations (23.6% saved)

Details

analyze270.0ms (3.5%)

sample34.0ms (0.4%)

simplify409.0ms (5.3%)

prune4.0ms (0.1%)

localize14.0ms (0.2%)

rewrite35.0ms (0.5%)

series286.0ms (3.7%)

simplify90.0ms (1.2%)

prune110.0ms (1.4%)

localize15.0ms (0.2%)

rewrite49.0ms (0.6%)

series472.0ms (6.1%)

simplify61.0ms (0.8%)

prune174.0ms (2.2%)

localize14.0ms (0.2%)

rewrite87.0ms (1.1%)

series541.0ms (7%)

simplify126.0ms (1.6%)

prune560.0ms (7.2%)

localize20.0ms (0.3%)

rewrite97.0ms (1.2%)

series426.0ms (5.5%)

simplify135.0ms (1.7%)

prune555.0ms (7.2%)

regimes755.0ms (9.7%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.4s (31.2%)

Profiling