Details

sample219.0ms

Algorithm

intervals

Results

84.0ms	90×	body	2560	valid
50.0ms	102×	body	1280	valid
49.0ms	55×	body	10240	exit
10.0ms	35×	body	640	valid
5.0ms	311×	pre	80	true
2.0ms	13×	body	320	valid
1.0ms	13×	body	80	valid
0.0ms	3×	body	160	valid

simplify93.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	13
1	101	13
2	245	13
3	697	13
4	3463	13
5	5001	13
done	5001	13

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.6b

localize17.0ms

Local error

Found 4 expressions with local error:

1.5b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.7b	(- (exp (* a eps)) 1.0)
3.0b	(- (exp (* b eps)) 1.0)
4.8b	(- (exp (* (+ a b) eps)) 1.0)

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`flip3--` `flip--`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
5×	`sub-neg` `associate-r` `associate-l` `distribute-lft-out--` `difference-of-squares`
4×	`frac-times`
3×	`diff-log`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-r/` `associate-l/`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

78.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
16.0ms	(- (exp (* a eps)) 1.0)
13.0ms	(- (exp (* b eps)) 1.0)
15.0ms	(- (exp (* (+ a b) eps)) 1.0)

series180.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
36.0ms	(- (exp (* a eps)) 1.0)
38.0ms	(- (exp (* b eps)) 1.0)
51.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify47.0ms

Counts

88 → 88

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	346	733
1	1449	673
2	5001	673
done	5001	673

prune366.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 50.1b

localize30.0ms

Local error

Found 4 expressions with local error:

4.2b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))))
4.8b	(- (exp (* (+ a b) eps)) 1.0)
14.0b	(* (pow eps 2) (pow b 2))
15.8b	(* (pow eps 3) (pow b 3))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
40×	`add-exp-log`
32×	`unswap-sqr`
28×	`unpow-prod-down`
22×	`prod-exp`
20×	`associate-r` `associate-l` `add-cbrt-cube` `sqr-pow`
16×	`*-un-lft-identity`
14×	`add-cube-cbrt` `cube-prod`
12×	`pow-to-exp` `pow-exp`
10×	`unpow2`
8×	`associate-/r/`
6×	`cbrt-unprod` `add-log-exp`
5×	`flip3--` `flip--`
4×	`pow1` `cbrt-undiv` `frac-times` `associate-*r/` `div-exp`
3×	`flip3-+` `flip-+`
2×	`cube-mult` `unpow3` `pow-prod-down` `associate-l/` `-commutative` `associate-/l/`
1×	`sub-neg` `frac-2neg` `times-frac` `diff-log` `clear-num` `associate-/r` `div-inv` `associate-/l` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 155

Calls

4 calls:

114.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))))
15.0ms	(- (exp (* (+ a b) eps)) 1.0)
22.0ms	(* (pow eps 2) (pow b 2))
21.0ms	(* (pow eps 3) (pow b 3))

series1.7s

Counts

4 → 12

Calls

4 calls:

1.6s	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))))
51.0ms	(- (exp (* (+ a b) eps)) 1.0)
39.0ms	(* (pow eps 2) (pow b 2))
65.0ms	(* (pow eps 3) (pow b 3))

simplify47.0ms

Counts

167 → 167

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	848	1789
1	5001	1488
done	5001	1488

prune720.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ (/ 1 b) (/ 1 a))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
7×	`distribute-lft-out`
6×	`times-frac`
4×	`div-inv`
3×	`add-sqr-sqrt` `add-cube-cbrt` `add-log-exp`
1×	`pow1` `add-exp-log` `+-commutative` `flip3-+` `frac-add` `sum-log` `add-cbrt-cube` `flip-+`

Counts

1 → 19

Calls

1 calls:

23.0ms

(+ (/ 1 b) (/ 1 a))

series11.0ms

Counts

1 → 3

Calls

1 calls:

11.0ms

(+ (/ 1 b) (/ 1 a))

simplify63.0ms

Counts

22 → 22

Iterations

Useful iterations: 3 (25.0ms)

Iter	Nodes	Cost
0	101	104
1	345	94
2	1153	91
3	2775	90
4	5001	90
done	5001	90

prune49.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
0.6b	(cbrt (+ (/ 1 b) (/ 1 a)))
0.6b	(cbrt (+ (/ 1 b) (/ 1 a)))
0.6b	(cbrt (+ (/ 1 b) (/ 1 a)))

rewrite231.0ms

Algorithm

rewrite-expression-head

Rules

139×	`*-un-lft-identity`
114×	`cbrt-prod`
81×	`distribute-lft-out`
60×	`div-inv`
42×	`times-frac`
37×	`add-sqr-sqrt`
33×	`cbrt-div` `swap-sqr`
29×	`add-cube-cbrt`
13×	`associate-r` `associate-l`
11×	`pow1` `flip3-+` `frac-add` `flip-+`
9×	`frac-times` `pow1/3`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
3×	`associate-r/` `associate-l/`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 159

Calls

4 calls:

162.0ms	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
18.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
19.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
22.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))

series373.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
90.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
87.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
89.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))

simplify57.0ms

Counts

171 → 171

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	389	1813
1	1557	1563
2	5001	1403
done	5001	1403

prune301.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

regimes285.0ms

Accuracy

0% (3.3b remaining)

Error of 3.5b against oracle of 0.1b and baseline of 3.5b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	3
1	9	3
done	9	3

end0.0ms

sample6.8s

Algorithm

intervals

Results

2.5s	2609×	body	2560	valid
1.7s	2039×	body	10240	exit
1.6s	3403×	body	1280	valid
282.0ms	1053×	body	640	valid
161.0ms	10041×	pre	80	true
63.0ms	340×	body	320	valid
26.0ms	464×	body	80	valid
15.0ms	133×	body	160	valid