Details

sample29.0ms

Algorithm

intervals

Results

8.0ms	234×	body	80	valid
4.0ms	9×	body	1280	valid
2.0ms	15×	body	640	valid
1.0ms	15×	body	320	valid
0.0ms	7×	body	160	valid
0.0ms	1×	body	2560	valid

simplify91.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (17.0ms)

Iter	Nodes	Cost
0	22	6
1	52	6
2	111	6
3	213	6
4	517	5
5	1051	5
6	2055	5
7	3280	5
8	5002	5

prune9.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 10.6b

Counts

2 → 2

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (- a t))
12.3b	(fma (/ y (- a t)) (- t z) (+ x y))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/r*`
4×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
3×	`associate-/l*`
2×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `fma-udef` `div-inv`

Counts

2 → 49

Calls

2 calls:

6.0ms	(/ y (- a t))
1.0ms	(fma (/ y (- a t)) (- t z) (+ x y))

series115.0ms

Counts

2 → 6

Calls

2 calls:

32.0ms	(/ y (- a t))
83.0ms	(fma (/ y (- a t)) (- t z) (+ x y))

simplify58.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	170	278
1	468	257
2	1400	257
3	5002	257

prune186.0ms

Filtered

55 candidates to 43 candidates (78.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	45	10	55
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	46	11	57

Merged error: 7.3b

Counts

57 → 11

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ y (- a t))
3.3b	(+ (* (/ y (- a t)) (- t z)) (+ x y))
10.2b	(* (/ y (- a t)) (- t z))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

68×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
47×	`add-cube-cbrt`
36×	`prod-diff`
31×	`times-frac`
22×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
21×	`associate-l`
10×	`add-exp-log` `frac-add` `add-cbrt-cube`
8×	`flip3--` `flip--` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
6×	`frac-times` `flip3-+` `associate-*r/` `flip-+`
5×	`pow1` `associate-r` `associate-/r*`
4×	`sub-neg` `associate-/r/`
3×	`expm1-log1p-u` `associate-l/` `sum-log` `log1p-expm1-u` `associate-/l`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`+-commutative` `associate-+r+` `fma-def` `frac-2neg` `pow-prod-down` `clear-num` `*-commutative`

Counts

3 → 157

Calls

3 calls:

6.0ms	(/ y (- a t))
19.0ms	(+ (* (/ y (- a t)) (- t z)) (+ x y))
14.0ms	(* (/ y (- a t)) (- t z))

series288.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(/ y (- a t))
103.0ms	(+ (* (/ y (- a t)) (- t z)) (+ x y))
156.0ms	(* (/ y (- a t)) (- t z))

simplify109.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	859	1392
1	4016	1146
2	5001	1146

prune471.0ms

Filtered

166 candidates to 120 candidates (72.3%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	157	9	166
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	160	17	177

Merged error: 7.3b

Counts

177 → 17

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt y)
0.8b	(* (/ (* (cbrt y) (cbrt y)) 1) (* (/ (cbrt y) (- a t)) (- t z)))
3.0b	(* (/ (cbrt y) (- a t)) (- t z))
9.2b	(+ (* (/ (* (cbrt y) (cbrt y)) 1) (* (/ (cbrt y) (- a t)) (- t z))) (+ x y))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

107×	`add-sqr-sqrt`
99×	`distribute-rgt-in` `*-un-lft-identity` `distribute-lft-in`
90×	`prod-diff`
85×	`add-cube-cbrt`
66×	`add-exp-log`
44×	`associate-+l+`
43×	`associate-l`
35×	`times-frac` `add-cbrt-cube`
33×	`prod-exp`
29×	`frac-times` `associate-*r/`
22×	`frac-add`
20×	`cbrt-unprod`
19×	`cbrt-prod`
18×	`div-exp`
15×	`flip3--` `flip--`
12×	`flip3-+` `flip-+`
11×	`pow1`
10×	`cbrt-undiv` `sub-neg` `associate-*l/`
9×	`add-log-exp`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`1-exp` `associate-r`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u`
3×	`sum-log` `unswap-sqr`
2×	`associate-/r/` `*-commutative` `div-inv`
1×	`+-commutative` `associate-+r+` `fma-def` `pow1/3`

Counts

4 → 280

Calls

4 calls:

1.0ms	(cbrt y)
21.0ms	(* (/ (* (cbrt y) (cbrt y)) 1) (* (/ (cbrt y) (- a t)) (- t z)))
17.0ms	(* (/ (cbrt y) (- a t)) (- t z))
31.0ms	(+ (* (/ (* (cbrt y) (cbrt y)) 1) (* (/ (cbrt y) (- a t)) (- t z))) (+ x y))

series1.1s

Counts

4 → 12

Calls

4 calls:

199.0ms	(cbrt y)
190.0ms	(* (/ (* (cbrt y) (cbrt y)) 1) (* (/ (cbrt y) (- a t)) (- t z)))
522.0ms	(* (/ (cbrt y) (- a t)) (- t z))
169.0ms	(+ (* (/ (* (cbrt y) (cbrt y)) 1) (* (/ (cbrt y) (- a t)) (- t z))) (+ x y))

simplify80.0ms

Algorithm

egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 1 (42.0ms)

Iter	Nodes	Cost
0	1731	4253
1	5002	3476

prune851.0ms

Filtered

292 candidates to 174 candidates (59.6%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	290	2	292
Fresh	2	13	15
Picked	1	0	1
Done	0	1	1
Total	293	16	309

Merged error: 7.3b

Counts

309 → 16

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt y)
0.5b	(cbrt y)
3.0b	(* (/ (cbrt y) (- a t)) (- t z))
11.2b	(fma (/ (* (cbrt y) (cbrt y)) 1) (* (/ (cbrt y) (- a t)) (- t z)) (+ x y))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
50×	`*-un-lft-identity`
36×	`add-cube-cbrt` `associate-l`
32×	`times-frac`
22×	`cbrt-prod`
18×	`prod-diff`
11×	`distribute-rgt-in` `distribute-lft-in`
9×	`add-exp-log`
8×	`add-cbrt-cube`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1`
5×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `flip--` `unswap-sqr`
2×	`frac-times` `sub-neg` `pow1/3` `associate-*r/` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `fma-udef` `div-inv`

Counts

4 → 122

Calls

4 calls:

1.0ms	(cbrt y)
1.0ms	(cbrt y)
17.0ms	(* (/ (cbrt y) (- a t)) (- t z))
1.0ms	(fma (/ (* (cbrt y) (cbrt y)) 1) (* (/ (cbrt y) (- a t)) (- t z)) (+ x y))

series1.1s

Counts

4 → 12

Calls

4 calls:

197.0ms	(cbrt y)
195.0ms	(cbrt y)
528.0ms	(* (/ (cbrt y) (- a t)) (- t z))
190.0ms	(fma (/ (* (cbrt y) (cbrt y)) 1) (* (/ (cbrt y) (- a t)) (- t z)) (+ x y))

simplify69.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	516	1106
1	2119	918
2	5002	906

prune433.0ms

Filtered

134 candidates to 97 candidates (72.4%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	127	7	134
Fresh	3	11	14
Picked	1	0	1
Done	1	0	1
Total	132	18	150

Merged error: 7.2b

Counts

150 → 18

regimes463.0ms

Accuracy

10.1% (5.0b remaining)

Error of 10.8b against oracle of 5.8b and baseline of 11.3b

bsearch57.0ms

Steps

Iters	Range		Point
9	1.2691783740187593e+232	4.821681246489376e+237	3.4126882859688763e+232

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	17
1	26	17

end0.0ms

sample684.0ms

Algorithm

intervals

Results

271.0ms	7379×	body	80	valid
58.0ms	456×	body	640	valid
39.0ms	241×	body	1280	valid
36.0ms	374×	body	320	valid
18.0ms	277×	body	160	valid
4.0ms	19×	body	2560	valid