Details

sample30.0ms

Algorithm

intervals

Results

12.0ms

256×

body

valid

simplify6.8s

Counts

1 → 1

Iterations

Useful iterations: 4 (124.0ms)

Iter	Nodes	Cost
0	16	21
1	33	20
2	79	20
3	201	20
4	405	19
5	766	19
6	1278	19
7	2257	19
8	4193	19
done	5000	19

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.7b

localize14.0ms

Local error

Found 3 expressions with local error:

0.8b	(fma x z (* y (- z b)))
1.0b	(fma a (+ t y) (fma x z (* y (- z b))))
26.9b	(/ (fma a (+ t y) (fma x z (* y (- z b)))) (+ (+ x t) y))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 59

Calls

3 calls:

1.0ms	(fma x z (* y (- z b)))
1.0ms	(fma a (+ t y) (fma x z (* y (- z b))))
71.0ms	(/ (fma a (+ t y) (fma x z (* y (- z b)))) (+ (+ x t) y))

series715.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(fma x z (* y (- z b)))
137.0ms	(fma a (+ t y) (fma x z (* y (- z b))))
537.0ms	(/ (fma a (+ t y) (fma x z (* y (- z b)))) (+ (+ x t) y))

simplify1.2s

Counts

68 → 68

Iterations

Useful iterations: 2 (108.0ms)

Iter	Nodes	Cost
0	90	1500
1	185	1471
2	530	1345
3	2162	1345
done	5000	1345

prune284.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 11.7b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ x t) y))
0.8b	(fma x z (* y (- z b)))
1.0b	(fma a (+ t y) (fma x z (* y (- z b))))
26.9b	(* (fma a (+ t y) (fma x z (* y (- z b)))) (/ 1 (+ (+ x t) y)))

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

60×	`*-un-lft-identity`
32×	`times-frac`
31×	`add-sqr-sqrt`
24×	`add-cube-cbrt`
21×	`associate-r` `distribute-lft-out`
17×	`add-exp-log`
11×	`add-cbrt-cube`
7×	`pow1`
5×	`associate-/r*`
4×	`expm1-log1p-u` `div-exp` `prod-exp` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `flip3-+` `1-exp` `cbrt-unprod` `flip-+` `fma-udef` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 109

Calls

4 calls:

58.0ms	(/ 1 (+ (+ x t) y))
0.0ms	(fma x z (* y (- z b)))
0.0ms	(fma a (+ t y) (fma x z (* y (- z b))))
127.0ms	(* (fma a (+ t y) (fma x z (* y (- z b)))) (/ 1 (+ (+ x t) y)))

series857.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ 1 (+ (+ x t) y))
49.0ms	(fma x z (* y (- z b)))
138.0ms	(fma a (+ t y) (fma x z (* y (- z b))))
611.0ms	(* (fma a (+ t y) (fma x z (* y (- z b)))) (/ 1 (+ (+ x t) y)))

simplify2.1s

Counts

121 → 121

Iterations

Useful iterations: 2 (121.0ms)

Iter	Nodes	Cost
0	129	2017
1	287	1805
2	823	1597
3	3622	1597
done	5000	1597

prune291.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 11.7b

localize18.0ms

Local error

Found 4 expressions with local error:

9.4b	(* (* (cbrt (fma a (+ t y) (fma x z (* y (- z b))))) (cbrt (fma a (+ t y) (fma x z (* y (- z b)))))) (/ (cbrt (fma a (+ t y) (fma x z (* y (- z b))))) (+ (+ x t) y)))
27.6b	(cbrt (fma a (+ t y) (fma x z (* y (- z b)))))
27.6b	(cbrt (fma a (+ t y) (fma x z (* y (- z b)))))
27.6b	(cbrt (fma a (+ t y) (fma x z (* y (- z b)))))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
36×	`associate-r`
32×	`times-frac`
29×	`add-sqr-sqrt`
25×	`cbrt-prod`
24×	`add-cube-cbrt`
18×	`distribute-lft-out`
16×	`add-exp-log`
10×	`add-cbrt-cube`
9×	`pow1`
6×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `pow-prod-down` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-/r/`
1×	`flip3-+` `associate-r/` `associate-l` `-commutative` `flip-+` `div-inv`

Counts

4 → 100

Calls

4 calls:

112.0ms	(* (* (cbrt (fma a (+ t y) (fma x z (* y (- z b))))) (cbrt (fma a (+ t y) (fma x z (* y (- z b)))))) (/ (cbrt (fma a (+ t y) (fma x z (* y (- z b))))) (+ (+ x t) y)))
1.0ms	(cbrt (fma a (+ t y) (fma x z (* y (- z b)))))
1.0ms	(cbrt (fma a (+ t y) (fma x z (* y (- z b)))))
1.0ms	(cbrt (fma a (+ t y) (fma x z (* y (- z b)))))

series1.5s

Counts

4 → 12

Calls

4 calls:

608.0ms	(* (* (cbrt (fma a (+ t y) (fma x z (* y (- z b))))) (cbrt (fma a (+ t y) (fma x z (* y (- z b)))))) (/ (cbrt (fma a (+ t y) (fma x z (* y (- z b))))) (+ (+ x t) y)))
318.0ms	(cbrt (fma a (+ t y) (fma x z (* y (- z b)))))
277.0ms	(cbrt (fma a (+ t y) (fma x z (* y (- z b)))))
280.0ms	(cbrt (fma a (+ t y) (fma x z (* y (- z b)))))

simplify1.3s

Counts

112 → 112

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	142	4398
1	399	4258
2	1425	3325
done	5000	3158

prune430.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 11.7b

localize23.0ms

Local error

Found 4 expressions with local error:

9.8b	(/ (* (cbrt (fma a (+ t y) (fma x z (* y (- z b))))) (cbrt (fma a (+ t y) (fma x z (* y (- z b)))))) (* (cbrt (+ (+ x t) y)) (cbrt (+ (+ x t) y))))
27.6b	(cbrt (fma a (+ t y) (fma x z (* y (- z b)))))
27.6b	(cbrt (fma a (+ t y) (fma x z (* y (- z b)))))
27.6b	(cbrt (fma a (+ t y) (fma x z (* y (- z b)))))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-exp-log`
12×	`cbrt-div`
9×	`cbrt-prod`
8×	`associate-/r/` `add-cbrt-cube`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`flip3-+` `flip-+`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `frac-times` `div-exp` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`associate-r/` `associate-l/`
1×	`frac-2neg` `times-frac` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 70

Calls

4 calls:

83.0ms	(/ (* (cbrt (fma a (+ t y) (fma x z (* y (- z b))))) (cbrt (fma a (+ t y) (fma x z (* y (- z b)))))) (* (cbrt (+ (+ x t) y)) (cbrt (+ (+ x t) y))))
1.0ms	(cbrt (fma a (+ t y) (fma x z (* y (- z b)))))
1.0ms	(cbrt (fma a (+ t y) (fma x z (* y (- z b)))))
1.0ms	(cbrt (fma a (+ t y) (fma x z (* y (- z b)))))

series13.6s

Counts

4 → 12

Calls

4 calls:

12.8s	(/ (* (cbrt (fma a (+ t y) (fma x z (* y (- z b))))) (cbrt (fma a (+ t y) (fma x z (* y (- z b)))))) (* (cbrt (+ (+ x t) y)) (cbrt (+ (+ x t) y))))
272.0ms	(cbrt (fma a (+ t y) (fma x z (* y (- z b)))))
235.0ms	(cbrt (fma a (+ t y) (fma x z (* y (- z b)))))
275.0ms	(cbrt (fma a (+ t y) (fma x z (* y (- z b)))))

simplify1.9s

Counts

82 → 82

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	124	2593
1	334	2490
2	959	2091
3	3060	1978
done	5001	1960

prune325.0ms

Pruning

10 alts after pruning (6 fresh and 4 done)

Merged error: 11.7b

regimes399.0ms

Accuracy

-5.1% (19.3b remaining)

Error of 27.4b against oracle of 8.1b and baseline of 26.5b

bsearch434.0ms

Steps

Iters	Range		Point
8	3.0376813422418597e+242	2.7149331643725744e+245	4.8305390600672115e+244
10	2.3595830904332568e+170	1.4707329520884118e+184	1.1811655993202686e+178
11	3.475438971074325e+61	1.3750260887017298e+85	3.9184516853750717e+61
9	1.359227237486475e-46	4.467925684565128e-41	4.4266847018442053e-41
5	-5.1211213003479313e+98	-1.3416769488648837e+98	-5.039519107897214e+98

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	82
1	39	82
done	39	82

end0.0ms

sample760.0ms

Algorithm

intervals

Results

353.0ms	7999×	body	80	valid
0.0ms	1×	body	320	valid