Details

sample31.0ms

Algorithm

intervals

Results

15.0ms

266×

body

valid

simplify17.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	26	8
1	39	8
2	51	8
3	61	8
4	65	8
5	65	8

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 17.6b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (/ (* y z) t))
5.2b	(/ (* y b) t)
5.4b	(/ (* y z) t)
10.9b	(/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

59×	`*-un-lft-identity`
26×	`times-frac`
22×	`distribute-lft-out`
20×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/r*`
6×	`associate-/l*` `add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `expm1-log1p-u` `flip3-+` `associate-/r/` `flip-+` `log1p-expm1-u`
3×	`fma-def` `frac-2neg` `clear-num` `div-inv`
2×	`frac-add` `prod-exp` `cbrt-unprod` `associate-/l/`
1×	`+-commutative` `sum-log`

Counts

4 → 112

Calls

4 calls:

5.0ms	(+ x (/ (* y z) t))
5.0ms	(/ (* y b) t)
5.0ms	(/ (* y z) t)
15.0ms	(/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))

series183.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ x (/ (* y z) t))
24.0ms	(/ (* y b) t)
19.0ms	(/ (* y z) t)
109.0ms	(/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))

simplify66.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	472	881
1	2005	817
2	5001	797

prune392.0ms

Filtered

124 candidates to 86 candidates (69.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	110	14	124
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	111	14	125

Merged error: 10.1b

Counts

125 → 14

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt t)
3.0b	(* (/ y (* (cbrt t) (cbrt t))) (/ b (cbrt t)))
5.4b	(/ (* y z) t)
10.9b	(/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (* (/ y (* (cbrt t) (cbrt t))) (/ b (cbrt t)))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
43×	`times-frac`
39×	`*-un-lft-identity`
32×	`add-exp-log`
31×	`add-cube-cbrt`
25×	`add-cbrt-cube`
22×	`associate-r`
14×	`cbrt-prod`
10×	`cbrt-undiv` `div-exp`
9×	`prod-exp` `cbrt-unprod`
8×	`associate-/r/`
7×	`associate-l`
6×	`pow1` `frac-add` `associate-/r*` `unswap-sqr`
5×	`flip3-+` `flip-+` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `distribute-lft-out` `add-log-exp`
3×	`frac-times` `associate-r/` `associate-l/`
2×	`frac-2neg` `clear-num` `associate-/l/`
1×	`pow1/3` `pow-prod-down` `*-commutative`

Counts

4 → 140

Calls

4 calls:

1.0ms	(cbrt t)
19.0ms	(* (/ y (* (cbrt t) (cbrt t))) (/ b (cbrt t)))
5.0ms	(/ (* y z) t)
13.0ms	(/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (* (/ y (* (cbrt t) (cbrt t))) (/ b (cbrt t)))))

series417.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(cbrt t)
57.0ms	(* (/ y (* (cbrt t) (cbrt t))) (/ b (cbrt t)))
19.0ms	(/ (* y z) t)
149.0ms	(/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (* (/ y (* (cbrt t) (cbrt t))) (/ b (cbrt t)))))

simplify117.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (100.0ms)

Iter	Nodes	Cost
0	806	1621
1	4063	1415
2	5001	1357

prune541.0ms

Filtered

152 candidates to 114 candidates (75.0%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	148	4	152
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	150	16	166

Merged error: 9.6b

Counts

166 → 16

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt t)
3.0b	(* (/ y (* (cbrt t) (cbrt t))) (/ b (cbrt t)))
4.0b	(fma (/ y t) z x)
10.9b	(/ (fma (/ y t) z x) (+ (+ a 1.0) (* (/ y (* (cbrt t) (cbrt t))) (/ b (cbrt t)))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
37×	`times-frac`
28×	`add-cube-cbrt` `*-un-lft-identity`
27×	`add-exp-log`
22×	`associate-r`
20×	`add-cbrt-cube`
14×	`cbrt-prod`
8×	`cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod`
7×	`associate-l`
6×	`pow1` `frac-add` `unswap-sqr`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `associate-r/` `associate-l/` `associate-/r` `div-inv` `associate-/l`
1×	`frac-2neg` `pow1/3` `pow-prod-down` `clear-num` `*-commutative` `fma-udef`

Counts

4 → 121

Calls

4 calls:

1.0ms	(cbrt t)
19.0ms	(* (/ y (* (cbrt t) (cbrt t))) (/ b (cbrt t)))
1.0ms	(fma (/ y t) z x)
8.0ms	(/ (fma (/ y t) z x) (+ (+ a 1.0) (* (/ y (* (cbrt t) (cbrt t))) (/ b (cbrt t)))))

series804.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(cbrt t)
60.0ms	(* (/ y (* (cbrt t) (cbrt t))) (/ b (cbrt t)))
42.0ms	(fma (/ y t) z x)
507.0ms	(/ (fma (/ y t) z x) (+ (+ a 1.0) (* (/ y (* (cbrt t) (cbrt t))) (/ b (cbrt t)))))

simplify94.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	670	1404
1	3147	1221
2	5001	1177

prune511.0ms

Filtered

133 candidates to 102 candidates (76.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	131	2	133
Fresh	1	14	15
Picked	1	0	1
Done	0	0	0
Total	133	16	149

Merged error: 9.6b

Counts

149 → 16

localize25.0ms

Local error

Found 4 expressions with local error:

6.2b	(* (/ 1 (* (cbrt (+ (+ a 1.0) (* (/ y (* (cbrt t) (cbrt t))) (/ b (cbrt t))))) (cbrt (+ (+ a 1.0) (* (/ y (* (cbrt t) (cbrt t))) (/ b (cbrt t))))))) (/ (fma (/ y t) z x) (cbrt (+ (+ a 1.0) (* (/ y (* (cbrt t) (cbrt t))) (/ b (cbrt t)))))))
10.1b	(cbrt (+ (+ a 1.0) (* (/ y (* (cbrt t) (cbrt t))) (/ b (cbrt t)))))
10.1b	(cbrt (+ (+ a 1.0) (* (/ y (* (cbrt t) (cbrt t))) (/ b (cbrt t)))))
10.1b	(cbrt (+ (+ a 1.0) (* (/ y (* (cbrt t) (cbrt t))) (/ b (cbrt t)))))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

176×	`cbrt-div`
132×	`frac-add`
109×	`frac-times`
88×	`flip3-+` `associate-/r/` `flip-+`
87×	`associate-l`
53×	`associate-r/` `associate-l/`
49×	`add-exp-log`
43×	`add-sqr-sqrt`
33×	`times-frac`
30×	`associate-r`
25×	`*-un-lft-identity`
22×	`add-cube-cbrt`
21×	`cbrt-prod`
20×	`prod-exp`
18×	`add-cbrt-cube`
15×	`div-exp`
9×	`unswap-sqr`
8×	`cbrt-unprod`
7×	`cbrt-undiv`
6×	`pow1`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`div-inv`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 223

Calls

4 calls:

72.0ms	(* (/ 1 (* (cbrt (+ (+ a 1.0) (* (/ y (* (cbrt t) (cbrt t))) (/ b (cbrt t))))) (cbrt (+ (+ a 1.0) (* (/ y (* (cbrt t) (cbrt t))) (/ b (cbrt t))))))) (/ (fma (/ y t) z x) (cbrt (+ (+ a 1.0) (* (/ y (* (cbrt t) (cbrt t))) (/ b (cbrt t)))))))
6.0ms	(cbrt (+ (+ a 1.0) (* (/ y (* (cbrt t) (cbrt t))) (/ b (cbrt t)))))
6.0ms	(cbrt (+ (+ a 1.0) (* (/ y (* (cbrt t) (cbrt t))) (/ b (cbrt t)))))
6.0ms	(cbrt (+ (+ a 1.0) (* (/ y (* (cbrt t) (cbrt t))) (/ b (cbrt t)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

411.0ms	(* (/ 1 (* (cbrt (+ (+ a 1.0) (* (/ y (* (cbrt t) (cbrt t))) (/ b (cbrt t))))) (cbrt (+ (+ a 1.0) (* (/ y (* (cbrt t) (cbrt t))) (/ b (cbrt t))))))) (/ (fma (/ y t) z x) (cbrt (+ (+ a 1.0) (* (/ y (* (cbrt t) (cbrt t))) (/ b (cbrt t)))))))
213.0ms	(cbrt (+ (+ a 1.0) (* (/ y (* (cbrt t) (cbrt t))) (/ b (cbrt t)))))
214.0ms	(cbrt (+ (+ a 1.0) (* (/ y (* (cbrt t) (cbrt t))) (/ b (cbrt t)))))
215.0ms	(cbrt (+ (+ a 1.0) (* (/ y (* (cbrt t) (cbrt t))) (/ b (cbrt t)))))

simplify95.0ms

Algorithm

egg-herbie

Counts

235 → 235

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1213	7509
1	5001	6945

prune1.7s

Filtered

235 candidates to 209 candidates (88.9%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	235	0	235
Fresh	0	15	15
Picked	0	1	1
Done	0	0	0
Total	235	16	251

Merged error: 9.6b

Counts

251 → 16

regimes618.0ms

Accuracy

46.5% (2.4b remaining)

Error of 13.1b against oracle of 10.7b and baseline of 15.1b

bsearch147.0ms

Steps

Iters	Range		Point
7	5.902529941233592e+26	8.735509020663321e+28	3.0702964098391594e+27
10	-1.6574561910326728e+129	-2.8227101307296217e+118	-9.172008906914828e+123

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	54	61
1	54	61

end0.0ms

sample677.0ms

Algorithm

intervals

Results

387.0ms

8257×

body

valid